data_source stringclasses 6
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | problem stringlengths 8 2.45k | prompt_messages listlengths 2 2 | gt stringlengths 1 428 |
|---|---|---|---|---|---|---|---|
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the greatest common divisor (GCD) of the numbers 5280 and 12155. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 55 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "12\\text{ min}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | I run at a constant pace, and it takes me 24 minutes to run to the store from my house. The store is 3 miles away from my house. If my friend's house is 1.5 miles away from my house, how many minutes will it take me to run from my house to my friend's house? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 12\text{ min} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "4.64 \\times 10^7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The approximate number 24,000 is accurate to the ______ place, and the scientific notation for 46,400,000 is ______. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4.64 \times 10^7 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "(-\\frac{3}{2}, +\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f\left(x\right)=|x-a|+|x+3|$.<br/>$(1)$ When $a=1$, find the solution set of the inequality $f\left(x\right)\geqslant 6$;<br/>$(2)$ If $f\left(x\right) \gt -a$, find the range of values for $a$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (-\frac{3}{2}, +\infty) |
numina_aops_forum | [
{
"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]... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $f:\mathbb{N}\mapsto\mathbb{R}$ be the function \[f(n)=\sum_{k=1}^\infty\dfrac{1}{\operatorname{lcm}(k,n)^2}.\] It is well-known that $f(1)=\tfrac{\pi^2}6$ . What is the smallest positive integer $m$ such that $m\cdot f(10)$ is the square of a rational multiple of $\pi$ ? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 42 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "n^2 + n = n(n + 1)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the following equations:
$1^2 + 1 = 1 \times 2$, $2^2 + 2 = 2 \times 3$, $3^2 + 3 = 3 \times 4$, …
Observing the series of equations above, what pattern can you find? Express this pattern using an algebraic formula. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | n^2 + n = n(n + 1) |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "19",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In an arithmetic sequence \(\left\{a_{n}\right\}\), if \(\frac{a_{11}}{a_{10}} < -1\), and the sum of its first \(n\) terms \(S_{n}\) has a maximum value. Then, when \(S_{n}\) attains its smallest positive value, \(n =\) ______ . | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 19 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "[0, +\\infty)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x) = x^2 + a\ln x$.
(1) When $a = -2$, determine the intervals of monotonicity and the extrema for the function $f(x)$;
(2) If $g(x) = f(x) + \ln x$ is a monotonically increasing function on $[1, +\infty)$, find the range of the real number $a$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | [0, +\infty) |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "(-\\infty, -1) \\cup (0, e)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given $f(x) = \begin{cases} \ln \frac{1}{x}, & x > 0 \\ \frac{1}{x}, & x < 0 \end{cases}$, then $f(f(e)) = \_\_\_\_$; the solution set of the inequality $f(x) > -1$ is $\_\_\_\_$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (-\infty, -1) \cup (0, e) |
numina_synthetic_amc | [
{
"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]... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a box with dimensions $5\text{-in} \times 4\text{-in}\times3\text{-in}$ and blocks with dimensions $1\text{-in} \times 2\text{-in} \times 2\text{-in}$, calculate the largest number of such blocks that can fit inside the box. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 12 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "\\operatorname{tg} 6\\beta - \\operatorname{tg} 4\\beta - \\operatorname{tg} 2\\beta = \\operatorname{tg} 6\\beta \\operatorname{tg} 4\\beta \\operatorname{tg} 2\\beta",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \(\tan 6 \beta - \tan 4 \beta - \tan 2 \beta = \tan 6 \beta \tan 4 \beta \tan 2 \beta\). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \operatorname{tg} 6\beta - \operatorname{tg} 4\beta - \operatorname{tg} 2\beta = \operatorname{tg} 6\beta \operatorname{tg} 4\beta \operatorname{tg} 2\beta |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "33.5 \\text{ winners}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | There are 100 red balls in a red box and 100 green balls in a green box. Eight red balls are transferred to the green box, and then the same number of balls are transferred from the green box to the red box. The balls in the boxes are thoroughly mixed. What is more likely now: drawing a green ball from the red box or a... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 33.5 \text{ winners} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "q=1 \\text{ or } q=-\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let the sequence \\(\{a_n\}\) be a geometric sequence, and let the sum of the first \\(n\\) terms be \\(S_n\\). If \\(S_3=3a_3\\), then the common ratio \\(q=\\)_______. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | q=1 \text{ or } q=-\frac{1}{2} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "D(2, -1)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given $A(1,-2)$, $B(2,1)$, $C(3,2)$, $D(x,y)$:
1. Find the coordinates of $3\overrightarrow {AB}-2\overrightarrow {AC}+\overrightarrow {BC}$.
2. If points $A$, $B$, $C$, $D$ form a parallelogram $ABCD$, find the coordinates of point $D$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | D(2, -1) |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "x = \\frac{7}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given two vectors $ \vec{a}=(1,2) $ and $ \vec{b}=(x,1) $:
(1) If the angle between $ \vec{a} $ and $ \vec{b} $ is acute, find the range of $x$.
(2) When $\vec{a}+2\vec{b}$ is orthogonal to $2\vec{a}-\vec{b}$, find the value of $x$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | x = \frac{7}{2} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\dfrac{14}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (1) Given the equation in terms of $x$, $kx^{2}+(2k+1)x+(k-1)=0$ has real roots, then the range of $k$ is __.
(2) On New Year's Day, students in the math interest group exchanged New Year's cards with each other, with each pair of students exchanging one card. Xiao Ming counted a total of 90 New Year's cards exchanged... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \dfrac{14}{3} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "①④",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given propositions:
\\(①\\) The range of the function \\(y=2^{x}(-1\leqslant x\leqslant 1)\\) is \\(\left[ \frac{1}{2},2\right]\\);
\\(②\\) To obtain the graph of the function \\(y=\sin (2x- \frac{\pi}{3})\\), it is only necessary to shift all points of the graph of the function \\(y=\sin 2x\\) to the right by \\(\... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | ①④ |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given $\overrightarrow{OA}=(2,3),\overrightarrow{OB}=(3,t)$, and $|\overrightarrow{AB}|=1$, find the real number $t$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The greatest common divisor of 98 and 63 is . | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 7 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "15x^2-10y^2+7xy",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Simplify:<br/>$(1)2a-\left(4a+5b\right)+2\left(3a-4b\right)$;<br/>$(2)5x^{2}-2(3y^{2}-5x^{2})+(-4y^{2}+7xy)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 15x^2-10y^2+7xy |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given \\(a \in \mathbb{R}\\), the line \\(l_{1}: x + 2y = a + 2\\) and the line \\(l_{2}: 2x - y = 2a - 1\\) intersect the circle \\(E: (x - a)^{2} + (y - 1)^{2} = 9\\) at points \\(A\\), \\(C\\) and \\(B\\), \\(D\\) respectively. Then, the area of the quadrilateral \\(ABCD\\) is \_\_\_\_\_\_\_\_. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 18 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "\\frac{1}{5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $\det \mathbf{A} = 5$ and $\det \mathbf{B} = 7,$ determine $\det (\mathbf{A} \mathbf{B})$ and $\det (\mathbf{A}^{-1})$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{1}{5} |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "98",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Systems of linear equations | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 98 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "-14",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate:<br/>$(1)(\frac{2}{3}-\frac{1}{4}-\frac{1}{6})×24$;<br/>$(2){(-2)}^{3}+[-9+{(-3)}^{2}×\frac{1}{3}]$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -14 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "25",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic sequence $\{a_{n}\}$. If $a_{1}=-2$ and $a_{2}+a_{6}=2$, then $S_{10}=$____. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 25 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "x = 5316750",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | When $0.53\overline{207}$ is expressed as a fraction in the form $\frac{x}{999900}$, what is the value of $x$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | x = 5316750 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "22",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | There are 6000 points inside a circle, none of which are collinear.
1. Can this circle be divided into 2000 regions, each containing exactly three points? If so, how can it be divided?
2. If the distances between any two points in each region are integers and do not exceed 9, considering triangles formed with these thr... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 22 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the minimum value of the fraction \( \frac{x}{y} \), if \( \sqrt{x-1} + \sqrt{y-1} = 1 \). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{1}{2} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "y^{2}=8x\\ \\text{or}\\ x^{2}=-4y",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that the vertex of a parabola is at the origin, the axis of symmetry is the coordinate axis, and the focus lies on the line $(x-2y-2=0)$, determine the standard equation of this parabola. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | y^{2}=8x\ \text{or}\ x^{2}=-4y |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "k+1=0, k=-1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the curve $y=kx+\ln x$ has a tangent line at the point $(1,k)$ that is parallel to the x-axis, calculate the value of $k$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | k+1=0, k=-1 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "1+ \\frac {1}{2}+ \\frac {1}{3}+…+ \\frac {1}{2^{n+1}-1} > \\frac {n+1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the following inequalities: $1+ \frac {1}{2}+ \frac {1}{3} > 1$, $1+ \frac {1}{2}+ \frac {1}{3}+…+ \frac {1}{7} > \frac {3}{2}$, $1+ \frac {1}{2}+ \frac {1}{3}+…+ \frac {1}{15} > 2…$, then according to this pattern, the $n$-th inequality can be conjectured as \_\_\_\_\_\_. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1+ \frac {1}{2}+ \frac {1}{3}+…+ \frac {1}{2^{n+1}-1} > \frac {n+1}{2} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\pi^{2}+1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)= \begin{cases} 0 &(x > 0) \\ \pi &(x=0) \\ \pi^{2}+1 &(x < 0) \end{cases}$, find the value of $f(-1)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \pi^{2}+1 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\frac{1}{6025}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the sequence $\{a_n\}$ where $a_{n+1} = \frac{a_n}{3a_n + 1}$, and $a_1 = 1$, find the value of $a_{2009}$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{1}{6025} |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A portion of the graph of $f(x)=px^2+qx+r$ is shown. The distance between grid lines on the graph is $1$ unit.
What is the value of $p+q+2r$?
The graph of $y=f(x)$ passes through points $(0, 9)$ and $(1, 6)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 15 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "-\\frac{1}{8}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Simplify first, then evaluate: $\left(\frac{a+1}{2a-2}-\frac{5}{2{a}^{2}-2}-\frac{a+3}{2a+2}\right)÷\frac{{a}^{2}}{{a}^{2}-1}$, where the value of $a$ is chosen as an appropriate integer from the solution set of the inequality system $\left\{\begin{array}{l}{a-\sqrt{5}＜0}\\{\frac{a-1}{2}＜a}\end{array}\right.$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -\frac{1}{8} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | 4 students are admitted by three universities: Zhongda, Huagong, and Huashi. If each university must admit at least one student, then there are a total of \_\_\_\_\_\_ different admission methods. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 36 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "9",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that point $P(a_n,a_{n+1})$ is on the curve $x-y+d^2=0$, and $a_1 > 0$, $a_1+a_2+…+a_{10}=30$, find the maximum value of $a_5 \cdot a_6$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 9 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | How many distinct prime factors does the sum of the positive divisors of $882$ have? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "-\\frac{\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A line has an angle of inclination of $\frac{5\pi}{6}$. Calculate the slope of the line. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -\frac{\sqrt{3}}{3} |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $p$, $q$, $r$, and $s$ be real numbers such that $|p-q|=3$, $|q-r|=4$, and $|r-s|=5$. Furthermore, assume $r > q$. What is the sum of all possible values of $|p-s|$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 24 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "\\frac{30!}{10! \\cdot 10! \\cdot 10! \\cdot 3!}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In how many ways can 30 different books be arranged into three stacks so that each stack contains 10 books? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{30!}{10! \cdot 10! \cdot 10! \cdot 3!} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\frac{3}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)=kx-1$, where $k$ is a real number randomly chosen from the interval $[-2,2]$, calculate the probability that $f(x)\leqslant 0$ for $x\in[0,1]$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{3}{4} |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "4 \\text{ and } 7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the natural numbers \(k\) of the form \(k=\frac{a^{2}+a b+b^{2}}{a b-1}\) where \(a\) and \(b\) are natural numbers such that \(a b \neq 1\). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4 \text{ and } 7 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "\\frac{9\\sqrt{2}}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Points $A$, $B$, $C$, $D$, and $E$ are located in 3-dimensional space with $AB = BC = CD = DE = EA = 3$ and $\angle ABC = \angle CDE = 90^\circ$, but $\angle DEA = 120^\circ$. The plane of triangle $ABC$ is perpendicular to $\overline{DE}$. What is the area of triangle $BDE$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{9\sqrt{2}}{2} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "S_{n} = 8 - \\frac{1}{2^{n+1} - 1} - \\frac{3n + 7}{2^n}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a geometric sequence $\{a_{n}\}$ with a common ratio $q \gt 1$, if $a_{2}+a_{3}+a_{4}=14$, and $a_{2}$, $a_{3}+1$, $a_{4}$ are the $1$st, $3$rd, and $5$th terms of an arithmetic sequence $\{b_{n}\}$.<br/>$(1)$ Find the general formulas for sequences $\{a_{n}\}$ and $\{b_{n}\}$;<br/>$(2)$ If ${c}_{n}=\frac{2{a}_{n... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | S_{n} = 8 - \frac{1}{2^{n+1} - 1} - \frac{3n + 7}{2^n} |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "\\int \\frac{dx}{x \\left(1 + \\ln^2 x \\right)} = \\arctan(\\ln x) + C, \\quad\n\\int \\frac{e^x \\, dx}{1 + e^{2x}} = \\arctan(e^x) + C, \\quad\n\\int \\frac{\\cos x \\, dx}{1 + \\sin^2 x} = \\arctan(\\sin x) + C",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the following integrals:
\[ \int \frac{d x}{x\left(1+\ln ^{2} x\right)}, \quad \int \frac{e^{x} d x}{1+e^{2 x}}, \quad \int \frac{\cos x d x}{1+\sin ^{2} x}. \] | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \int \frac{dx}{x \left(1 + \ln^2 x \right)} = \arctan(\ln x) + C, \quad
\int \frac{e^x \, dx}{1 + e^{2x}} = \arctan(e^x) + C, \quad
\int \frac{\cos x \, dx}{1 + \sin^2 x} = \arctan(\sin x) + C |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "(0, 2)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the interval(s) where the function $f(x)=x^{3}-3x^{2}+1$ is strictly decreasing. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (0, 2) |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\frac{7\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given an ellipse with the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ and an eccentricity of $e = \frac{\sqrt{2}}{3}$, the focal length is $2\sqrt{2}$.
(1) Find the equation of the ellipse.
(2) Point $A$ is a point on the ellipse, and ${F_1}, {F_2}$ are the two foci of the ellipse. If $\angle {F_1}A{... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{7\sqrt{3}}{3} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "60",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the expansion of $({3+x}){({x+\frac{1}{x}})^6}$, the constant term is ____ (answer with a number). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 60 |
numina_synthetic_amc | [
{
"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]... | math | {
"ground_truth": "(-\\infty, -3) \\text{ or (3, \\infty)}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the complete set of $x$-values satisfying the inequality $\frac{x^2 - 9}{x^2 - 4} > 0$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (-\infty, -3) \text{ or (3, \infty)} |
numina_synthetic_amc | [
{
"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]... | math | {
"ground_truth": "-\\frac{20}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $a + 2 = b + 4 = c + 6 = d + 8 = a + b + c + d + 10$. Solve for the value of $a + b + c + d$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -\frac{20}{3} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\frac{x^2}{2} - \\frac{y^2}{7} = 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the line $l: y = x + m$ ($m \in \mathbb{R}$), and the hyperbola $E: \frac{x^2}{2} - \frac{y^2}{b^2} = 1$ ($b > 0$).
(1) If the line $l$ is parallel to one of the asymptotes of the hyperbola $E$, find the eccentricity of the hyperbola $E$.
(2) If the line $l$ passes through the right focus $F_2$ of the hyperbola... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{x^2}{2} - \frac{y^2}{7} = 1 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "-\\frac{1}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $\sin(\alpha - \frac{\pi}{6}) = \frac{1}{3}$, find the value of $\cos(\alpha + \frac{\pi}{3})$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -\frac{1}{3} |
numina_synthetic_amc | [
{
"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]... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the value of $15$ quarters and $20$ dimes is equal to the value of $10$ quarters, $n$ dimes, and $5$ nickels, find the value of $n$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 30 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the arithmetic sequence $\{a_n\}$, $a_3=2$, $a_5=7$, find $a_7$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 12 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Call a number greater than 25 semi-prime if it is the sum of any two distinct prime numbers. What is the maximum number of consecutive semi-prime numbers that can be semi-prime? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 5 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\{-2, -18, -72\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Define: For three distinct negative integers, if the arithmetic square root of the product of any two of them is an integer, then these three numbers are called "combination square numbers." For example, for the numbers $-1$, $-4$, $-9$, the square roots of the products $(-1) \times (-4)$, $(-1) \times (-9)$, and $(-4)... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \{-2, -18, -72\} |
numina_synthetic_amc | [
{
"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]... | math | {
"ground_truth": "1480",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the sum of consecutive integers starting from $85$ to $100$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1480 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "(3\\sqrt{2}, -3\\sqrt{2}, 0)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Convert the point $(\rho,\theta,\phi) = \left( 6, \frac{7 \pi}{4}, \frac{\pi}{2} \right)$ in spherical coordinates to rectangular coordinates. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (3\sqrt{2}, -3\sqrt{2}, 0) |
numina_synthetic_amc | [
{
"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]... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Consider the cubic polynomial equation $3x^3 - 9x^2 - 48x + 8 = 0$. Calculate the sum of all its roots. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3 |
numina_amc_aime | [
{
"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]... | math | {
"ground_truth": "\\$782",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the charity sells $140$ benefit tickets for a total of $$2001$, and some tickets sell for full price and the rest sell for half price, calculate the amount of money raised by the full-price tickets. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \$782 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "\\frac{2008}{1005}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the sum of the squares of the solutions to
\[\left| x^2 - x + \frac{1}{2010} \right| = \frac{1}{2010}.\] | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{2008}{1005} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\left\\{x|x=k\\pi- \\frac{\\pi}{3},k\\in\\mathbb{Z}\\right\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $y=A\sin (\omega x+\varphi)$, where $x\in\mathbb{R}$, $A > 0$, $\omega > 0$, $|\varphi| < \frac{\pi}{2}$, if the coordinates of one of the highest points on the graph of the function are $\left(\frac{\pi}{6}, 3\right)$, and the coordinates of the symmetry center adjacent to it are $\left(-\frac{\pi}{... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \left\{x|x=k\pi- \frac{\pi}{3},k\in\mathbb{Z}\right\} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "m\\leq 4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the sets $A=\{x|-2\leq x\leq 7\}$ and $B=\{x|m+1\leq x\leq 2m-1\}$. If $A\cup B=A$, find the range of the real number $m$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | m\leq 4 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\frac{4\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given in the Cartesian coordinate system $xOy$, with $O$ as the pole and the positive half-axis of $x$ as the polar axis, the parametric equation of curve $C_{1}$ is:
$$
\begin{cases}
x=1+\frac{\sqrt{2}}{2}t \\
y=-2+\frac{\sqrt{2}}{2}t \\
\end{cases},
$$
and the polar equation of curve $C_{2}$ is: $\rho^{2}(1+\sin^... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{4\sqrt{3}}{3} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "(0, 3)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In triangle $\triangle ABC$, $a$, $b$, $c$ are the lengths of the sides opposite to angles $A$, $B$, $C$ respectively. Given that $\sin ^{2}A+\sin ^{2}C=\sin ^{2}B+\sin A\sin C$. Find:<br/>
$(Ⅰ)$ The measure of angle $B$;<br/>
$(Ⅱ)$ If $\triangle ABC$ is an acute triangle and $b=\sqrt{3}$, find the range of values for ... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | (0, 3) |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\left[0,1\\right]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given sets $A=\{x|x^{2}-2x \gt 0\}$ and $B=\{y|y=\sin x\}$, calculate $(\complement _{R}A)\cap B$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \left[0,1\right] |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "-1 + i",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the complex number $z$ such that
\[ |z - 2| = |z + 4| = |z + 2i|.\] | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -1 + i |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | How many real numbers \( x \) are solutions to the following equation? \[ |x-1| = |x-2| + |x-3| + |x-4| \] | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 2 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the area of the region bounded by the graph of $r = 2\sec \theta,$ the graph of $r = 2\csc \theta,$ the $x$-axis, and the $y$-axis. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 4 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | How many integers are there in the solution set of $|x-3| \leq 7.5$? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 15 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A certain garden charges $10$ yuan for each ticket, which can be used only once. In consideration of different needs of people and to attract more visitors, the garden has introduced a new ticketing method of "buying a personal annual pass" (the annual pass can be used by the holder for one year from the date of purcha... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 30 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "1 \\text{ or } 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine all positive integers \( n \) such that the equation \( x^{3} + y^{3} + z^{3} = n x^{2} y^{2} z^{2} \) has a positive integer solution \((x, y, z)\). | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1 \text{ or } 3 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\begin{cases} x=1+ \\frac{1}{2}t \\\\ y=5+ \\frac{\\sqrt{3}}{2}t \\end{cases}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A line passes through point M(1, 5) and has a slope angle of $\frac{\pi}{3}$. Determine the parametric equation of this line, with the displacement t from the fixed point M to the moving point P as the parameter. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \begin{cases} x=1+ \frac{1}{2}t \\ y=5+ \frac{\sqrt{3}}{2}t \end{cases} |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "36",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Two individuals, named A and B, start cycling simultaneously from point A to point B. Cyclist A's speed is 1.2 times that of Cyclist B's speed. After riding 4 kilometers, Cyclist B's bike has a malfunction, causing a delay equivalent to the time he would take to ride one-sixth of the total distance. After fixing the bi... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 36 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "50",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Sarah owns 20 rare stamps, and she calculates that 4 of these stamps are worth a total of $10. Assuming the price per stamp remains constant, what is the total value of her entire collection of stamps? | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 50 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "5R^2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A circle with radius \( R \) is inscribed in an isosceles trapezoid. The upper base of the trapezoid is half of its height. Find the area of the trapezoid. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 5R^2 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\frac{3}{2}, \\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the circle $x^2+y^2=9$, point $A(1,1)$ is inside the circle, and $P$, $Q$ are moving points on the circle such that $\angle PAQ=90^\circ$, $M$ is the midpoint of $PQ$.
(1) Find the equation of the trajectory curve $C$ of point $M$.
(2) Let $E(\frac{9}{2}, \frac{1}{2})$, $D(\frac{1}{2}, \frac{1}{2})$, determine wh... | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{3}{2}, \frac{1}{2} |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "x=4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the circle $x^{2}+y^{2}-4x+2y-3=0$ and a point $M(4,-8)$ outside the circle.
(1) Find the coordinates of the circle center and the radius length;
(2) Draw a line through point $M$ intersecting the circle at points $A$ and $B$. If $AB=4$, find the equation of line $AB$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | x=4 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x) = \begin{cases} \log_{3}(x-1), & x>1 \\ 3^{x}+2, & x\leq1 \end{cases}$, find the value of $f(f(\log_{3}2))$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 1 |
numina_olympiads | [
{
"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]... | math | {
"ground_truth": "3495250",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the sum of the first 10 elements that appear both in the arithmetic progression $\{4,7,10,13, \ldots\}$ and in the geometric progression $\{10,20,40,80, \ldots\}$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 3495250 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The distance from point $A(-2,1)$ to the $y$-axis can be calculated using the formula $|x|$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 2 |
numina_synthetic_math | [
{
"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]... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | For each pair of real numbers where $a \ne b$, define the operation $\star$ as \[
(a \star b) = \frac{a + b}{a - b}.
\] Calculate the value of $((2 \star 3) \star 5)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | 0 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "-26",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x) = x^5 + \sin x + \tan^3 x - 8$, and $f(-2) = 10$, find the value of $f(2)$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | -26 |
numina_cn_k12 | [
{
"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]... | math | {
"ground_truth": "\\frac{5}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given vectors $a=(-1,2)$ and $b=(m,1)$, if vector $a+2b$ is parallel to vector $2a-b$, calculate the dot product of $a$ and $b$. | [
{
"content": "You are a mathematical reasoning assistant. For each problem, follow these steps strictly:\n\n1. Solve the problem using step-by-step reasoning and output the final answer within \\boxed{}.\n2. Perform a self-evaluation:\n - You may include reasoning to verify correctness.\n - However, your fi... | \frac{5}{2} |
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