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eurus2_ground_truth_with_system

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AI2 Adapt Dev 46

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If the inequality $x + \\frac{4}{x - a} \\geq 5$ holds for all $x \\in (a, +\\infty)$, find the minimum value of the real number $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given vectors $\\overrightarrow{a}=(2,6)$ and $\\overrightarrow{b}=(-1,\\lambda)$, find the value of $\\lambda$ such that $\\overrightarrow{a}$ is parallel to $\\overrightarrow{b}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "How many ways are there to put 7 balls into 3 boxes if the balls are not distinguishable but the boxes are, with the constraint that no box can be empty?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Calculate the value of the expression:\n$$\\frac{1}{3}\\times9\\times\\frac{1}{27}\\times81\\times\\frac{1}{243}\\times729\\times\\frac{1}{2187}\\times6561\\times\\frac{1}{19683}\\times59049.$$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "On a line, there are blue and red points, with at least 5 red points. It is known that on any segment with endpoints at red points, containing a red point inside, there are at least 4 blue points. Additionally, on any segment with endpoints at blue points, containing 3 blue points inside, there are at least 2 red points. What is the maximum number of blue points that can be on a segment with endpoints at red points, that does not contain other red points?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The coefficient of $x^6$ in the expansion of $(1+x)^8$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Maria buys 5 apples, each priced at $0.75. If she pays with a $10 bill, calculate the amount of change that Maria will receive.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "\nIn an exam, 153 people scored no more than 30 points, with an average score of 24 points. 59 people scored no less than 80 points, with an average score of 92 points. The average score of those who scored more than 30 points is 62 points. The average score of those who scored less than 80 points is 54 points. How many people participated in this exam?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that in triangle $\\triangle ABC$, the three interior angles satisfy $2B=A+C$, and $AB=1$, $BC=4$, then the length of the median $AD$ on side $BC$ is ____.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The notation $[x]$ stands for the greatest integer that is less than or equal to $x$. Calculate $[2.7]$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find all values of $a$ such that the lines given by\n\\[\\begin{pmatrix} 1 \\\\ 3 \\\\ 0 \\\\ a \\end{pmatrix} + t \\begin{pmatrix} 2 \\\\ 4 \\\\ 1 \\\\ 3 \\end{pmatrix}\\]\nand\n\\[\\begin{pmatrix} 3 \\\\ 4 \\\\ 1 \\\\ 0 \\end{pmatrix} + u \\begin{pmatrix} 4 \\\\ 5 \\\\ 2 \\\\ 1 \\end{pmatrix}\\]\nare skew in 4-dimensional space.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Out of 500 participants in a remote math olympiad, exactly 30 did not like the problem conditions, exactly 40 did not like the organization of the event, and exactly 50 did not like the method used to determine the winners. A participant is called \"significantly dissatisfied\" if they were dissatisfied with at least two out of the three aspects of the olympiad. What is the maximum number of \"significantly dissatisfied\" participants that could have been at this olympiad?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that the angle between line $a$ and plane $\\alpha$ is $30^\\circ$, and $P$ is a fixed point in space, construct line $l$ through $P$ such that the angle between $l$ and both $a$ and $\\alpha$ is $45^\\circ$. How many such lines $l$ can be constructed?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the least positive integer $n$ such that when $3^n$ is written in base $143$, its two right-most digits in base $143$ are $01$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given propositions p: If $a > b$, then $\\frac{1}{a} < \\frac{1}{b}$; proposition q: $\\frac{1}{ab} < 0 \\Leftrightarrow ab < 0$. Here are four compound propositions: ①$p \\lor q$; ②$p \\land q$; ③$(\\neg p) \\land (\\neg q)$; ④$(\\neg p) \\lor (\\neg q)$. The number of true propositions among these is __________.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If $i$ is the imaginary unit and $z(1+i)=|i+1|$, determine the imaginary part of $z$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A, B, and C have some apples in total, and the total number is less than 100. If A gives $\\frac{1}{6}$ of his apples to B and $\\frac{1}{4}$ of his apples to C, they all end up with the same number of apples. How many apples did A originally have at most, and how many more apples did B originally have compared to C?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $f(n)$ be the integer closest to $\\sqrt[3]{n}$. Find $\\sum_{k=1}^{4095}\\frac 1{f(k)}.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given a box containing 3 screw base bulbs and 7 bayonet base bulbs, all of which have the same shape and power and are placed with their bases down, calculate the probability that the electrician gets a bayonet base bulb on his third try.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If the complex number $z$ satisfies $z\\cdot i=2-i$, then $|z|=$ ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given: $\\sin \\left(\\alpha+ \\frac {\\pi}{4}\\right)+2\\sin \\left(\\alpha- \\frac {\\pi}{4}\\right)=0$. \n$(1)$ Find the value of $\\tan \\alpha$; \n$(2)$ If $\\tan \\left( \\frac {\\pi}{4}-\\beta\\right)= \\frac {1}{3}$, find the value of $\\tan (\\alpha+\\beta)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "\nDecompose into a Fourier series the periodic functions:\n1) \\( f(x)=x^{2} \\) for \\( -\\pi \\leq x < \\pi \\) with \\( f(x)=f(x+2\\pi) \\).\n\nUsing the resulting decomposition, find the sum of the series:\na) \\( 1-\\frac{1}{2^{2}}+\\frac{1}{3^{2}}-\\frac{1}{4^{2}}+\\ldots \\)\nb) \\( 1+\\frac{1}{2^{2}}+\\frac{1}{3^{2}}+\\frac{1}{4^{2}}+\\ldots \\)\n\n2) \\( \\varphi(x)=x^{2} \\) for \\( 0 < x < \\pi \\) with \\( \\varphi(x)=\\varphi(x+\\pi) \\).\n\n3) \\( u=\\cos \\frac{x}{2} \\) for \\( 0 < x \\leq 2\\pi \\) with \\( u(x)=u(x+2\\pi) \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "$(1)$ A positive number $m$ has two square roots, which are $3-a$ and $2a+1$. Find the value of $m$. \n$(2)$ Given that the cube root of $5a+2$ is $3$, and the arithmetic square root of $3a+b-1$ is $4$, where $c$ is the integer part of $\\sqrt{13}$. Find the square root of $3a-b+c$. \n$(3)$ If $a=\\sqrt{2-b}+\\sqrt{b-2}-3$, find the cube root of $a+b$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "For $-1<r<1$, let $T(r)$ denote the sum of the geometric series \\[15+15r+15r^2+15r^3+\\cdots .\\]Let $b$ between $-1$ and $1$ satisfy $T(b)T(-b) = 2250$. Find $T(b)+T(-b)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If \\(y = mx + k\\), determine the distance between points \\((a, b)\\) and \\((c, d)\\) in terms of \\(a, c,\\) and \\(m\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Simplify the expression\n\\[\n\\frac{(\\sqrt{2} + 1)^{\\sqrt{3} - 1}}{(\\sqrt{2} - 1)^{\\sqrt{3} + 1}}\n\\]\nand write your answer in the form \\( a + b \\sqrt{c} \\), where \\( a, b, \\) and \\( c \\) are positive integers, and \\( c \\) is not divisible by the square of a prime.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Three candles can burn for 30, 40, and 50 minutes respectively (but they are not lit simultaneously). It is known that the three candles are burning simultaneously for 10 minutes, and only one candle is burning for 20 minutes. How many minutes are there when exactly two candles are burning simultaneously?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If the one-variable quadratic equation $k{x^2}-3x-\\frac{9}{4}=0$ has two distinct real roots with respect to $x$, calculate the smallest possible value of the integer $k$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The mathematicians of the ancient Greek Pythagorean school studied various polygonal numbers, such as triangular numbers $(1)$, $(3)$, $(6)$, $(10)$, $(…)$, with the $n$-th triangular number being $\\dfrac {n(n+1)}{2}= \\dfrac {1}{2}n^{2}+ \\dfrac {1}{2}n$. Let $N(n,k)$ represent the $n$-th $k$-sided polygonal number $(k\\geqslant 3)$. The following lists some expressions for the $n$-th $k$-sided polygonal number:\nTriangular numbers $N(n,3)= \\dfrac {1}{2}n^{2}+ \\dfrac {1}{2}n$\nSquare numbers $N(n,4)=n^{2}$\nPentagonal numbers $N(n,5)= \\dfrac {3}{2}n^{2}- \\dfrac {1}{2}n$\nHexagonal numbers $N(n,6)=2n^{2}-n$\n$…$\nWe can conjecture the expression for $N(n,k)$ and use it to calculate $N(8,12)=$ _____ .\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that the complex number $z$ is a root of the quadratic equation $x^2 - 2x + 2 = 0$, find the value of $|z|$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The equation of the tangent line to the graph of the function $f\\left(x\\right)=x^{4}-2x^{3}$ at the point $\\left(1,f\\left(1\\right)\\right)$ is $y=-2x+1$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that for all real numbers \\( x \\) and \\( y \\), the following equation holds:\n\n\\[ f(x) f(y) + f(x+y) = x y \\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find all integers \\( k \\) such that there exists an integer \\( x \\) satisfying the equation \\(\\sqrt{39-6 \\sqrt{12}} + \\sqrt{k x(k x + \\sqrt{12}) + 3} = 2k\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "What is the measure of the smaller angle between the hands of a 12-hour clock at 10:40 am, in degrees? Express your answer as a decimal to the nearest tenth.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A Swiss cross consists of five unit squares, one in the center and four on the sides. Determine the smallest natural number \\( n \\) with the following property: For every \\( n \\) points inside or on the edge of a Swiss cross, there are always two whose distance is less than 1.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "What is the value of $\\frac{18!}{6!12!}$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A coin is flipped ten times, and the sequence of heads and tails occurring is recorded. How many distinct sequences are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Determine the positive integer values of \\( x \\) and \\( y \\) that satisfy the equation\n\n$$\n(x - 6)(y - 6) = 18\n$$\n\nBased on this, find the right-angled triangles with integer sides where the perimeter tripled equals twice the area.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "From 4 high-quality items and 1 defective item, two items are randomly selected. Calculate the probability that exactly one high-quality item and one defective item are chosen.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If $\\cos \\theta = \\frac{3}{5},$ then find $\\cos 2 \\theta.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "How many 9-digit palindromes can be formed using the digits 1, 1, 2, 2, 2, 3, 3, 3, 3?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "For each prime number \\( p \\), find the largest natural power of \\( p \\), denoted by \\( p^k \\), such that \\( p^k \\) divides \\( (p^2)! \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The function \\( g(x) \\) satisfies\n\\[\ng(x) - 3 g \\left( \\frac{1}{x} \\right) = 3^x\n\\]\nfor all \\( x \\neq 0 \\). Find \\( g(3) \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given $f(x)= \\begin{cases} \\sin x,x\\in[0,1] \\\\ x^{2},x\\in[1,2] \\end{cases}$, find the value of $\\int_{0}^{2}f(x)dx$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that $| \\vec{OA} | = 1$, $| \\vec{OB} | = m$, and $\\angle AOB = \\frac{3}{4} \\pi$, point $C$ lies within $\\angle AOB$ and $\\vec{OA} \\cdot \\vec{OC} = 0$. If $\\vec{OC} = 2\\lambda \\vec{OA} + \\lambda \\vec{OB}$ ($\\lambda \\neq 0$), then find the value of $m$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Ann has exactly 30 pieces of fruit. She needs to distribute these equally among her 4 friends. What is the smallest number of pieces she should take away so she can distribute the remaining fruits equally?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Brand X soda now advertises, \"We will give you 25% more soda than Brand Y for a total price that is 15% less than Brand Y's price!\" What is the ratio of the unit price of Brand X soda to the unit price of Brand Y soda? Express your answer as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Two cards are chosen at random from a standard 52-card deck. What is the probability that both cards are numbers (2 through 10) totaling to 14?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Compute \\((1 + i)^6.\\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If a number is selected at random from the set of all five-digit numbers in which the sum of the digits is equal to 42, determine the probability that this number will be divisible by 11.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "At what angle do the curves \\( x^{2} + y^{2} = 16 \\) and \\( y^{2} = 6x \\) intersect?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Consider rectangle $ABCD$ with vertices $A(0, 0)$, $B(0, 6)$, $C(x, 6)$, and $D(x, 0)$, where the perimeter of the rectangle is 40 units. Find the value of $x$, given $x > 0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "To determine if an integer, $n$, is prime, one must ensure that none of the primes less than or equal to the square root of $n$ divide $n$. If you want to check that a number between 1000 and 1100 is prime using this rule, what is the largest prime divisor you need to test?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A cinema is showing four animated movies: Toy Story, Ice Age, Shrek, and Monkey King. The ticket prices are 50 yuan, 55 yuan, 60 yuan, and 65 yuan, respectively. Each viewer watches at least one movie and at most two movies. However, due to time constraints, viewers cannot watch both Ice Age and Shrek. Given that there are exactly 200 people who spent the exact same amount of money on movie tickets today, what is the minimum total number of viewers the cinema received today?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Determine the number of solutions to\n\\[3\\cos^2 x - 8\\cos x + 3 = 0\\] in the range $0 \\le x \\le 2\\pi$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "\na) In how many different ways can we paint the circles in the letter \"O,\" not necessarily using all 3 colors?\n\nb) In how many different ways can we paint the circles in the letter \"E,\" necessarily using all 3 colors?\n\nc) In how many different ways can we paint the letter \"B\" such that circles connected by a segment must have different colors? (The three circles aligned vertically have TWO segments separating them).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the result of $(1011101_2 + 1101_2) \\times 101010_2 \\div 110_2$. Express your answer in base 2.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "A hiker starts at a base camp and first travels 15 miles north, then 8 miles east, then 3 miles south, and finally 4 miles west. Calculate the distance from the base camp where the hiker ends up after these movements.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let \\(x, y, z\\) be real numbers such that \\(x + y + z = 7\\) and \\(xy + xz + yz = 12.\\) Find the largest possible value of \\(x.\\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let \\( d(n) \\) represent the number of positive divisors of the positive integer \\( n \\). Define \\( f(n)=\\frac{d(n)}{\\sqrt[3]{n}} \\). There exists a unique positive integer \\( N \\) such that for any positive integer \\( n \\neq N \\), \\( f(N) > f(n) \\) holds. Find the sum of the digits of \\( N \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The mathematician Fibonacci, while studying the problem of rabbit reproduction, discovered a sequence of numbers: \\(1, 1, 2, 3, 5, 8, 13, \\cdots\\). The characteristic of this sequence is that the first two numbers are both 1, and starting from the third number, each number is equal to the sum of the two preceding numbers. A sequence formed in this way is called the Fibonacci sequence, denoted as \\(\\{a_n\\}\\). Calculate the following expression using the Fibonacci sequence:\n$$\n\\begin{array}{l}\n\\left(a_{1} a_{3}+a_{2} a_{4}+a_{3} a_{5}+\\cdots+a_{2019} a_{2021}\\right)- \\\\\n\\left(a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+\\cdots+a_{2020}^{2}\\right) \\\\\n=\n\\end{array}\n$$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Consider the line \\( y = \\dfrac{1}{2}x + 3 \\) and another line \\( L \\) that runs parallel to the given line and is \\( 5 \\) units away from it. The correct equation for line \\( L \\) could be:\nA) \\( y = \\dfrac{1}{2}x + 3 + \\dfrac{5\\sqrt{5}}{2} \\)\nB) \\( y = \\dfrac{1}{2}x + 3 - \\dfrac{5\\sqrt{5}}{2} \\)\nC) \\( y = \\dfrac{1}{2}x + 5 \\)\nD) \\( y = \\dfrac{1}{2}x \\)\nE) \\( y = \\dfrac{1}{2}x - 2 \\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the Cartesian coordinate system, if the graph of the function y = x is rotated counterclockwise around the origin by $90^{\\circ}$ and then shifted up by 1 unit, determine the resulting equation of the line.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $A$ be a point on the parabola $y = x^2 - 4x + 7,$ and let $B$ be a point on the line $y = 2x - 3.$ Find the shortest possible distance $AB.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $f(x)$ be a polynomial such that\n\\[f(x^2 + 1) = x^4 + 4x^2.\\]\nFind $f(x^2 + 2)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given $\\tan \\theta = 3,$ find\n\\[\\frac{2 - 2\\cos \\theta}{\\sin \\theta} - \\frac{\\sin \\theta}{2 + 2\\cos \\theta}.\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given two sets $A = \\{x \\,|\\, x^2 - 2x - 3 \\geq 0\\}$ and $B = \\{x \\,|\\, m-2 \\leq x \\leq m+2, m \\in \\mathbb{R}\\}$:\n1. Find $\\mathbb{Z} \\cap \\complement_{\\mathbb{R}} A$.\n2. If $B \\subseteq A$, find the range of the real number $m$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the function $t(x)$ with a domain $\\{0, 1, 2, 3\\}$ and a range $\\{1, 3, 5, 7\\}$. Another function $u(x)$ has a domain $\\{2, 3, 4, 5\\}$ and is defined by $u(x) = x - 1$. Compute the sum of all possible values of $u(t(x))$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "\nFind the indefinite integral:\n\n$$\n\\int \\frac{x^{3}+6 x^{2}+9 x+6}{(x+1)^{2}\\left(x^{2}+2 x+2\\right)} d x\n$$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In the sequence $\\left\\{a_{n}\\right\\}$, if $a_{1} = 3$ and $n a_{n} = (n + 1) a_{n+1}$, then $a_{n} = ?$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The real function $f$ has the property that, whenever $a,$ $b,$ $n$ are positive integers such that $a + b = 2^n,$ the equation\n\\[f(a) + f(b) = n^3\\] holds. What is $f(2048)$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given two lines $l_1: 3x+2ay-1=0$ and $l_2: ax-y+2=0$. If $l_1 \\perp l_2$, then $a= \\boxed{\\text{?}}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Three flasks contain concentrated acid: 10 g in the first flask, 20 g in the second flask, and 30 g in the third flask. There is also a fourth flask containing water. If some amount of water from the fourth flask is added to the first flask, and the remaining water is poured into the second flask, then the acid in the first flask will constitute $\\frac{1}{20}$ of the mixture, and in the second flask, the acid will constitute $\\frac{7}{30}$ of the mixture. What fraction will the acid constitute in the third flask if all the water from the fourth flask is poured into it?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Five guys each have a positive integer (the integers are not necessarily distinct). The greatest common divisor of any two guys' numbers is always more than 1, but the greatest common divisor of all the numbers is 1. What is the minimum possible value of the product of the numbers?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let the reciprocals of the roots of $7x^2 + 4x + 9$ be $\\gamma$ and $\\delta$. Evaluate $\\gamma + \\delta$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "When \\( n \\) fair dice are thrown, the probability of obtaining a sum of 2005 and the probability of obtaining a sum of \\( S \\) are both equal to a positive number \\( p \\). Find the smallest possible value of \\( S \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The region consisting of all points in three-dimensional space within $4$ units of line segment $\\overline{CD}$ has volume $544\\pi$. Calculate the length of $CD$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that\n\\[\n\\frac{1}{x}+\\frac{1}{y}=4, \\quad x+y+xy=3,\n\\]\ncompute $x^3+y^3$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Calculate the value of $\\frac{17!}{7!10!}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In triangle $\\triangle ABC$, $2\\sin A \\cos B + b \\sin 2A + 2\\sqrt{3} a \\cos C = 0$. \n$(1)$ Find the measure of angle $C$. \n$(2)$ If $AC = 2$, $CD = \\sqrt{3}$, and point $D$ is the midpoint of $AB$, find the area of triangle $\\triangle BCD$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the function $f(x) = x^2$, then the limit $\\lim_{{\\Delta x} \\to 0} \\frac{f(\\Delta x)-f(0)}{\\Delta x}$ equals to \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Using the digits 1, 2, 3, 4, and 5, form a three-digit number without repetition and calculate the total number of possible three-digit numbers.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that the conic sections $C_{1}: mx^{2}+ny^{2}=1 (n>m>0)$ and $C_{2}: px^{2}-qy^{2}=1 (p>0, q>0)$ share common foci $F_{1}$, $F_{2}$. Point $M$ is a common point of $C_{1}$ and $C_{2}$, and satisfies $\\angle F_{1}MF_{2}=90^{\\circ}$. If the eccentricity of the conic section $C_{1}$ is $\\frac{3}{4}$, then determine the eccentricity of $C_{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic sequence $\\{a_{n}\\}$. Given $a_{2}=11$ and $S_{10}=40$. \n$(1)$ Find the general formula for $\\{a_{n}\\}$. \n$(2)$ Determine the sum $T_{n}$ of the absolute values of the first $n$ terms of the sequence $\\{|a_{n}|\\}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If the one-variable quadratic equation $x^{2}+bx-2=0$ has one root at $x=2$, find the value of $b$ and the other root of the equation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the restriction on the area of the field. Let the area of the field be \\( \\mathrm{S} \\) hectares, then \\( 10 \\times 300 \\times S \\leq 10000 \\).\n\n\\[ \\mathrm{S} \\leq \\frac{10}{3} \\]\n\nLet \\( 2a = -b \\), then \\( a = -\\frac{b}{2} \\).\n\nConsider \\( |6|y|+3| \\); the value of this expression is obviously not less than three.\n\nThen \\( 2|2|x|-b| \\leq 9 \\), hence \\( \\mathrm{b} \\geq -4.5 \\).\n\nFor \\( b > 4.5 \\), the point \\( (0, 0) \\) does not lie inside the bounded region, which contradicts the logical sense of the problem. Thus, we have a limit from \\(-4.5\\) to 4.5. Considering that the area increases with the value of \\( \\mathrm{b} \\) and we need only integer values, we have a finite set of parameters: \\( \\pm 4, \\pm 3, \\pm 2, \\pm 1, 0 \\).\n\nProceeding in ascending order, let \\( \\mathrm{b} = -4 \\):\n\n\\[ 2(2x+4) + (6y+3) = 12 \\]\n\\[ x = 0, y = \\frac{1}{6} \\]\n\\[ y = 0, x = \\frac{1}{4} \\]\n\\[ S = 2 \\times \\frac{1}{6} \\times \\frac{1}{4} = \\frac{1}{12} < \\frac{10}{3}, a = 2 \\]\n\nLet \\( b = -3 \\):\n\n\\[ 4x + 6 + 6y + 3 = 12 \\]\n\\[ 4x + 6y = 3 \\]\n\\[ x = 0, y = \\frac{1}{2} \\]\n\\[ y = 0, x = \\frac{3}{4} \\]\n\\[ S = 2 \\times \\frac{1}{2} \\times \\frac{3}{4} = \\frac{3}{4} < \\frac{10}{3}, a = 1.5 \\, \\text{ - not an integer} \\]\n\nLet \\( b = -2 \\):\n\n\\[ 4x + 4 + 6y + 3 = 12 \\]\n\\[ 4x + 6y = 5 \\]\n\\[ x = 0, y = \\frac{5}{6} \\]\n\\[ y = 0, x = \\frac{5}{4} \\]\n\\[ S = 2 \\times \\frac{5}{6} \\times \\frac{5}{4} = \\frac{25}{12} < \\frac{10}{3}, a = 1 \\]\n\nLet \\( b = -1 \\):\n\n\\[ 4x + 2 + 6y + 3 = 12 \\]\n\\[ 4x + 6y = 7 \\]\n\\[ x = 0, y = \\frac{7}{6} \\]\n\\[ y = 0, x = \\frac{7}{4} \\]\n\\[ S = 2 \\times \\frac{7}{6} \\times \\frac{7}{4} = \\frac{49}{12} > \\frac{10}{3}; \\]\n\\[ \\text{ - not suitable} \\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Expand the expression $-2(x+3)(x-2)(x+1)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given a rectangular garden measuring 10 feet by 7 feet, find the total number of strawberries Maria can harvest, where she plants 5 strawberry plants per square foot and each plant yields 12 strawberries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The quadratic polynomials \\( f(x) \\) and \\( g(x) \\) are such that\n\n\\[\n\\begin{aligned}\n& f(2) \\\\\n& g(2)\n\\end{aligned}=\\begin{aligned}\n& f(3) \\\\\n& g(3)\n\\end{aligned}=2\n\\]\n\nFind \\( f(1) \\), given that \\( g(1) = 2 \\), \\( f(5) = 7 \\), and \\( g(5) = 2 \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The minimum value of the function $f\\left(x\\right)=\\frac{1}{3}x^{3}-x^{2}$ on the interval $\\left[-1,1\\right]$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "If the shopper saves $\\textdollar{3.75}$ when buying a coat on sale and the final price paid for the coat was $\\textdollar{50}$, determine the percentage that the shopper saved.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given that angle $\\alpha$ is in the second quadrant and $\\tan \\alpha = -\\frac{1}{2}$, find $\\sin \\alpha$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "At Highland Academy, there are 25 players on the soccer team. All players are enrolled in either physics or mathematics, or both. If there are 15 players taking physics and 6 players are enrolled in both subjects, how many players are taking mathematics?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "In the expansion of $(x + a)^n$, where $x$, $a$, and $n$ are constants, the third and fourth terms are 126 and 504, respectively. The exponent $n$ is known to be 8. Determine the value of $(x + a)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given the function $f(x)= \\begin{cases} f[f(x+5)], & x < 100 \\\\ x-3, & x \\geqslant 100 \\end{cases}$, find the value of $f(97)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The perimeter of an isosceles triangle is $60cm$, with the two equal sides being $x cm$ and the base being $y cm$. Please write down the relationship between $y$ and $x$ as ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Given $m$ and $n$ are two different lines, and $\\alpha$ and $\\beta$ are two different planes, consider the following propositions: \n① If $m \\subset \\alpha$, $n \\parallel \\alpha$, then $m \\parallel n$; \n② If $m \\parallel \\alpha$, $m \\parallel \\beta$, then $\\alpha \\parallel \\beta$; \n③ If $m \\perp \\alpha$, $m \\perp n$, then $n \\parallel \\alpha$; \n④ If $m \\perp \\alpha$, $m \\perp \\beta$, then $\\alpha \\parallel \\beta$; \nThe number of true propositions is     .\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "The function $f(x)=3\\sin \\left(x+ \\frac{\\pi}{6}\\right)$ reaches its maximum value at $x=\\theta$. Then, calculate $\\tan \\theta$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Find the focus of the parabola $x = -\\frac{1}{4} y^2.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]

[ { "content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n", "role": "system" }, { "content": "Sally now has five red cards numbered $1$ through $5$ and five blue cards numbered $4, 5.5, 6, 7, 8$. She attempts to stack the cards so that the colors alternate and each red card divides evenly into each neighboring blue card (where possible since 5.5 isn’t an integer). How does she arrange the cards, and what is the sum of the numbers on the middle three cards?\nA) 15\nB) 16\nC) 17\nD) 18\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }, { "content": "I am a dummy message", "role": "user" } ]