data_source stringclasses 6
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | problem stringlengths 20 2.2k | prompt_messages listlengths 2 2 | gt stringlengths 1 1.03k |
|---|---|---|---|---|---|---|---|
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": "c = -15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the value of $c$ if $x\cdot(3x+1) - c > 0$ if and only when $x \in \left(-\frac{5}{3}, 3\right)$. | [
{
"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... | c = -15 |
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{479}{600}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In a two-day math competition, Charlie and Delta both attempted a total of 600 points. Charlie scored 200 points out of 400 attempted on the first day, and 160 points out of 200 attempted on the second day. Delta, who did not attempt 400 points on the first day, scored a positive integer number of points each day, and ... | [
{
"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{479}{600} |
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": "0.35 \\text{ kg}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A cup filled with water is poured into an empty can. If 2 cups of water are poured in, the total weight of the can and water is 0.6 kilograms; if 5 cups of water are poured in, the total weight is 0.975 kilograms. How much does the empty can weigh? | [
{
"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... | 0.35 \text{ kg} |
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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given $a$ is a real number, and $(2+ai)(a-2i)=-4i$, calculate the value of $a$. | [
{
"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 |
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"
} | Given the complex number $z=a^2+a-2+(a^2-3a+2)i$ is a pure imaginary number, find 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... | -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": "121.5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Lee can make 36 cookies with 4 cups of flour. How many cookies can he make with 7 cups of flour if he increases his cookie output by 50% per cup of flour increase? | [
{
"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... | 121.5 |
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": "10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the central angle of a regular polygon inscribed in a circle is $36^{\circ}$, calculate the number of sides of this regular polygon. | [
{
"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... | 10 |
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": "7 \\text{ inches}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Either increasing the radius or the height of a cylinder by seven inches will result in the same volume. The original height of the cylinder is three inches. What is the original radius in inches? | [
{
"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 \text{ inches} |
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": "f\\left(x_1\\right)+f\\left(x_2\\right)+\\cdots+f\\left(x_{n}\\right) \\leqslant n f\\left(\\frac{x_{1}+x_{2}+\\cdots+x_{n}}{n}\\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Suppose the function \( f(x) \) for the interval \( (a, b) \) [note: this interval can be open, closed, or half-open and half-closed] has the property for any two sets of values \( x_{1}, x_{2} \) and \( y_{1}, y_{2} \) in the interval with \( x_{1} + x_{2} = y_{1} + y_{2} \) that:
\[
\begin{array}{l}
f\left(x_{1}\righ... | [
{
"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... | f\left(x_1\right)+f\left(x_2\right)+\cdots+f\left(x_{n}\right) \leqslant n f\left(\frac{x_{1}+x_{2}+\cdots+x_{n}}{n}\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": "108^{2/5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the value of $x$ that satisfies $\sqrt[3]{2x\sqrt{x^3}} = 6$. | [
{
"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... | 108^{2/5} |
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": "10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $2^x + 2^x + 2^x + 2^x + 2^x + 2^x = 2048$, 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... | 10 |
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_2 = 3 - \\sqrt{14}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a quadratic equation in terms of $x$: $kx^{2}-(2k+4)x+k-6=0$ has two distinct real roots.<br/>$(1)$ Find the range of values for $k$;<br/>$(2)$ When $k=1$, solve the equation using the completing the square method. | [
{
"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_2 = 3 - \sqrt{14} |
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": "8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the minimum number of Sportloto (6 out of 49) cards you need to buy to ensure that at least one number is guessed in at least one of them? | [
{
"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... | 8 |
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 \\operatorname{ctg} 4\\alpha",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \(\operatorname{ctg} \alpha - \operatorname{tg} \alpha - 2 \operatorname{tg} 2 \alpha = 4 \operatorname{ctg} 4 \alpha\). | [
{
"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 \operatorname{ctg} 4\alpha |
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[ \\frac{1}{2},2 \\right]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x) = 2^{x-b}$, where $2 \leqslant x \leqslant 4$ and $b$ is a constant, whose graph passes through the point $(3,1)$, determine the range of $f(x)$. | [
{
"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... | \left[ \frac{1}{2},2 \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": "\\{x | \\frac{1}{2} \\leqslant x \\leqslant \\frac{5}{2}\\}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | For any real numbers $a (a \neq 0)$ and $b$, the inequality $|a+b|+|a-b| \geqslant M \cdot |a|$ always holds. Let $m$ be the maximum value of the real number $M$.
(1) Find the value of $m$;
(2) Solve the inequality $|x-1|+|x-2| \leqslant m$. | [
{
"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... | \{x | \frac{1}{2} \leqslant x \leqslant \frac{5}{2}\} |
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": "(x-1)^2 + \\left(y - \\frac{3}{2}\\right)^2 = \\frac{13}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a circle \( C: x^{2} + y^{2} = 24 \) and a line \( l: \frac{x}{12} + \frac{y}{8} = 1 \), let \( P \) be a point on \( l \). The ray \( OP \) intersects the circle at point \( R \). Also, point \( Q \) lies on \( OP \) and satisfies the condition \( |OQ| \cdot |OP| = |OR|^2 \). As point \( P \) moves along \( l \)... | [
{
"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-1)^2 + \left(y - \frac{3}{2}\right)^2 = \frac{13}{4} |
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{120}{13}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In $\triangle XYZ$, $XY = 13$, $XZ = 12$, and $YZ = 5$. A circle $S$ is internally tangent to $XY$ at a point $M$ which is $4$ units from $X$, and also passes through $Z$. Determine the length of the segment $QR$ where $Q$ and $R$ are the points of intersection, distinct from $Z$, of circle $S$ with sides $XZ$ and $YZ$... | [
{
"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{120}{13} |
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": "f(t) = 10t + 8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The line $y = 2x - 30$ is parameterized by $(x,y) = (f(t), 20t - 14)$. Determine the function $f(t)$. | [
{
"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... | f(t) = 10t + 8 |
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{3}{5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the maximum rate at which the function \( u(M) = \frac{10}{x^2 + y^2 + z^2 + 1} \) can increase as the point \( M(x, y, z) \) passes through the point \( M_0(-1, 2, -2) \)? In which direction should the point \( M \) move as it passes through the point \( M_1(2, 0, 1) \) for the function \( u(M) \) to decrease ... | [
{
"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}{5} |
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}{2}\\left(1 - \\frac{1}{\\sqrt[3]{500}}\\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the sum:
\[\sum_{n=3}^{500} \frac{1}{n \sqrt[3]{n-2} + (n-2) \sqrt[3]{n}}.\] | [
{
"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... | \frac{1}{2}\left(1 - \frac{1}{\sqrt[3]{500}}\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": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Five people can paint a room in 8 hours. How many more people are required to paint the room in 6 hours, assuming each person paints at the same rate? | [
{
"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_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": "8",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the largest positive integer \( n \) such that there exist \( n \) lattice points on the coordinate plane, and any 3 points form a triangle whose centroid is not a lattice point. | [
{
"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... | 8 |
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{5}{8}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $\sin A + \sin B = \frac{3}{2}$ and $\cos A + \cos B = 1$, what is the value of $\cos(A-B)$? | [
{
"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}{8} |
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": "2019",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the value of \( f(2019) \), given that \( f(x) \) satisfies the following three conditions:
1. \( f(x) > 0 \) for any \( x > 0 \)
2. \( f(1) = 1 \)
3. \( f(a+b) \cdot (f(a) + f(b)) = 2 f(a) \cdot f(b) + a^2 + b^2 \) for any \( a, b \in \mathbb{R} \) | [
{
"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... | 2019 |
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": "C) 10",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In an organization, there are five committees. According to the organization's rules:
1. Every member must belong to exactly two different committees.
2. Each pair of committees should have exactly one unique member.
Determine the total number of members in the organization.
A) 8
B) 9
C) 10
D) 12 | [
{
"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... | C) 10 |
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 {n}{2n+1}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the sequence $\{a\_n\}$, $a\_1=1$, $a\_{n+1}=a\_n+c$ ($c$ is a constant, $n∈N^{*}$), and $a\_1$, $a\_2$, $a\_5$ form a geometric sequence with a common ratio not equal to $1$.
(1) Find the value of $c$;
(2) Let $b\_n= \frac {1}{a\_n a\__{n+1}}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted... | [
{
"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 {n}{2n+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{n}{n+1}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given an arithmetic sequence $\{a\_n\}$ with the sum of the first $n$ terms denoted as $S\_n$. It is known that $S\_5 = 5S\_2$ and $2a\_1 + 1 = a\_3$.
1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $\{b\_n\} = \frac{1}{a\_n a\_{n+1}}\}$. Find the sum of the first $n$ terms, denoted as $T\_n$, 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... | \frac{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": "(x, y) = (-4, 2), (-12, 3), (5, 20), (6, 12), (8, 8)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine all pairs \((x, y)\) of integers with \(x \leq y\) for which \(\frac{1}{x} + \frac{1}{y} = \frac{1}{4}\). | [
{
"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... | (x, y) = (-4, 2), (-12, 3), (5, 20), (6, 12), (8, 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": "(1,2]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let the set $M=\{y|y=2\sin x, x \in [-5,5]\}$, and the set $N=\{x|y=\log_{2}(x-1)\}$. Find the intersection $M \cap N$. | [
{
"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... | (1,2] |
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": "-1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate $\left(\frac{1-i}{\sqrt{2}}\right)^{44}$. | [
{
"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_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{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the value of $\sin 50^{\circ}\cos 20^{\circ}-\cos 50^{\circ}\sin 20^{\circ}$. | [
{
"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{1}{2} |
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": "141",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \(AD\), \(BE\), and \(CF\) be segments sharing a common midpoint, forming a \(60^\circ\) angle with each pair, and having lengths \(AD = 7\), \(BE = 10\), and \(CF = 18\). Let \(K\) denote the sum of the areas of the six triangles \(\triangle ABC\), \(\triangle BCD\), \(\triangle CDE\), \(\triangle DEF\), \(\triang... | [
{
"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... | 141 |
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 = 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Draw a line through point P(3, -1) such that points A(2, -3) and B(4, 5) are equidistant from it. What is the equation of this 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... | x = 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": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given sets $A=\{1, 2, 3, 4\}$ and $B=\{0, 1, 2, 4, 5\}$, with the universal set $U=A \cup B$, determine the number of elements in the set $\overline{U}(A \cap B)$. | [
{
"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... | 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": "0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | For a positive integer $p$, define the positive integer $n$ to be $p$-safe if $n$ differs in absolute value by more than $3$ from all multiples of $p$. Find the number of positive integers less than or equal to $10,000$ which are simultaneously $5$-safe, $7$-safe, and $11$-safe. | [
{
"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": "2000",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A factory has produced 5,000 units of a certain product from three different production lines: A, B, and C. To check the quality of this batch of products, it has been decided to use stratified sampling. If the numbers of units sampled from production lines A, B, and C are in the ratio of 1:2:2, then production line 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... | 2000 |
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": "2001",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The expression $\frac{k^{2}}{1.001^{k}}$ reaches its maximum value with which natural number $k$? | [
{
"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... | 2001 |
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": "\\begin{pmatrix} 3/5 \\\\ -1/5 \\end{pmatrix}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A line is given by $y = 3x - 2$. Every vector on this line, when projected onto a vector $\mathbf{w}$, results in a constant vector $\mathbf{p}$. Determine the vector $\mathbf{p}$. | [
{
"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{pmatrix} 3/5 \\ -1/5 \end{pmatrix} |
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": "-1005",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the value of $y$ for which $(2010 + 2y)^2 = 4y^2$? | [
{
"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... | -1005 |
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": "16",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | At a math competition, a team of $8$ students has $2$ hours to solve $30$ problems. If each problem needs to be solved by $2$ students, on average how many minutes can a student spend on a problem? | [
{
"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... | 16 |
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": "62",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A two-digit number is a multiple of 2. When 1 is added to it, it becomes a multiple of 3; when 2 is added to it, it becomes a multiple of 4; and when 3 is added to it, it becomes a multiple of 5. What is this two-digit number? $\qquad$ . | [
{
"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... | 62 |
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"
} | Given the function $f(x)$ on $\mathbb{R}$ satisfies $f(x) = 2f(2-x) - x^2 + 8x - 8$, then $f'(1) = \boxed{?}$. | [
{
"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": "75.7^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \(A = (-3, 1, 5)\), \(B = (-4, 0, 2)\), and \(C = (-5, 0, 3)\). Compute \(\angle ABC\), in degrees. | [
{
"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... | 75.7^\circ |
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": "719",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | There are a certain number of identical plastic bags that can be nested within each other. If all the other bags are inside one of the bags, we call this situation a "bag of bags." Calculate the number of ways to make a "bag of bags" from 10 bags.
Explanation: Use parentheses to denote a bag.
If we had one bag, the w... | [
{
"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... | 719 |
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": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | \[2013\cdot Guangdong College Entrance Examination\] Let the sequence $\{a_n\}$ be a geometric sequence with the first term 1 and common ratio -2, then $a_1 + |a_2| + a_3 + |a_4| = \_\_\_\_\_\_\_\_$. | [
{
"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... | 15 |
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": "700000",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Two distinct natural numbers end in 5 zeros and have exactly 42 divisors. Find their sum. | [
{
"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... | 700000 |
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": "7920",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate $\binom{12}{10} \times 5!$. | [
{
"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... | 7920 |
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": "10999",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | (from The Good Soldier Svejk) Senior military doctor Bautze exposed $abccc$ malingerers among $aabbb$ draftees who claimed not to be fit for the military service. He managed to expose all but one draftees. (He would for sure expose this one too, if the lucky guy was not taken by a stroke at the very moment when the... | [
{
"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... | 10999 |
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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $A = (1,0)$ and $B = (-3, 4)$. Let $P$ be a point on the parabola $y^2 = 4x$. Find the smallest possible value of $AP + BP$. | [
{
"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_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[4, \\frac{9}{2}\\right]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the functions $f(x)=\ln(x-1)+x-2$ and $g(x)=x^2-ax-a+8$, where $f(x)$ and $g(x)$ are "adjacent zero functions", determine 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... | \left[4, \frac{9}{2}\right] |
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^\\circ",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $O$ be the center of the circumscribed circle around the triangle $ABC$. Find the angle $OAC$ if: a) $\angle B=50^{\circ}$; b) $\angle B=126^{\circ}$. | [
{
"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^\circ |
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": "\\cos<5\\overrightarrow{a}-\\overrightarrow{b},\\overrightarrow{a}>=\\frac{13}{14}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with an angle of $120^{\circ}$ between them, $|\overrightarrow{a}|=1$ and $|\overrightarrow{b}|=3$,
(I) Find the value of $|5\overrightarrow{a}-\overrightarrow{b}|$
(II) Find the cosine value of the angle between the vector $5\overrightarrow{a}-\overrighta... | [
{
"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... | \cos<5\overrightarrow{a}-\overrightarrow{b},\overrightarrow{a}>=\frac{13}{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": "(-\\infty, 1)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $f(x) = x^3$, then the range of values of $x$ for which $f(x) < 1$ 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) |
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": "32, 64, 96",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the first digit of a two-digit natural number \( N \) is multiplied by 4, and the second digit is multiplied by 2, then the sum of the resulting numbers equals \( \frac{N}{2} \). Find \( N \) (list all solutions). | [
{
"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... | 32, 64, 96 |
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 : 12",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the diagram, \(ABCD\) is a parallelogram, \(M\) is the midpoint of \(AB\), and \(X\) is the point of intersection of \(AC\) and \(MD\). What is the ratio of the area of \(MBCX\) to the area of \(ABCD\)? | [
{
"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 : 12 |
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{2\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 (a > 0, b > 0)$ passes through the focus of the parabola $(C_2: y^2 = 2px (p > 0))$, and the asymptotes of the hyperbola and the axis of symmetry of the parabola form an equilateral triangle, calculate the eccentricity 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{2\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": "-20",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The quadratic $4x^2 - 40x + 100$ can be written in the form $(ax+b)^2 + c$, where $a$, $b$, and $c$ are constants. What is $2b-3c$? | [
{
"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... | -20 |
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": "21",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the frequency of drawing a white chess piece stabilizes to 0.3 after repeatedly drawing and replacing the pieces, estimate the number of black chess pieces in the bag. | [
{
"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... | 21 |
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": "17",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The greatest common divisor of 1343 and 816 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... | 17 |
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(1,-2\\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The coordinates of the point $\left(1,-2\right)$ with respect to the origin are ____. | [
{
"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(1,-2\right) |
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": "2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In an acute-angled triangle \( ABC \), the altitude \( AA_1 \) is drawn. \( H \) is the orthocenter of triangle \( ABC \). It is known that \( AH = 3 \), \( A_1H = 2 \), and the radius of the circumcircle of triangle \( ABC \) is 4. Find the distance from the center of this circumcircle to \( H \). | [
{
"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_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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a line $f$ and two parallel lines $e$ and $g$ that are each at a unit distance from $f$ on either side. Let points $E$, $F$, and $G$ be on lines $e$, $f$, and $g$ respectively, such that the triangle formed by $E$, $F$, and $G$ has a right angle at $F$. What is the length of the altitude of the triangle from poin... | [
{
"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_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": "2240",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | How many odd numbers between $1000$ and $9999$ have distinct digits? | [
{
"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... | 2240 |
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": "8\\pi - 9",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the first quadrant, there is a region known as the comet's tail region, surrounded by the quarter-circle of radius 6 with center (0,0), a quarter square with side 6, and a smaller quarter-circle of radius 2 centered at (0,2). The vertexes of the quarter square align with the quadrant axes. Determine the area of the ... | [
{
"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... | 8\pi - 9 |
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": "11",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the smallest value of $\left|36^{m}-5^{n}\right|$, where $m$ and $n$ are positive integers. | [
{
"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... | 11 |
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": "29",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The numbers $1, 2, \dots ,N$ are arranged in a circle where $N \geq 2$ . If each number shares a common digit with each of its neighbours in decimal representation, what is the least possible value of $N$ ? $
\textbf{a)}\ 18
\qquad\textbf{b)}\ 19
\qquad\textbf{c)}\ 28
\qquad\textbf{d)}\ 29
\qquad\textbf{e)}\ \te... | [
{
"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... | 29 |
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": "81",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \( A = \{1, 2, 3, 4, 5, 6\} \). Find the number of distinct functions \( f: A \rightarrow A \) such that \( f(f(f(n))) = n \) for all \( n \in A \). | [
{
"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... | 81 |
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": "27",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Medians $\overline{DP}$ and $\overline{EQ}$ of $\triangle DEF$ are perpendicular. If $DP = 27$ and $EQ = 36$, and the centroid $G$ divides medians in the ratio 3:2 (i.e., $DG:GP = EG:GQ = 3:2$), what is the length of ${DE}$? | [
{
"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... | 27 |
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": "16\\pi",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the area enclosed by the region defined by the equation \(x^2 + y^2 + 8x - 6y = -9\)? | [
{
"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... | 16\pi |
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}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In isosceles trapezoid $ABCD$ where $AB$ (shorter base) is 10 and $CD$ (longer base) is 20. The non-parallel sides $AD$ and $BC$ are extended to meet at point $E$. What is the ratio of the area of triangle $EAB$ to the area of trapezoid $ABCD$? | [
{
"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_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"
} | For the prime $p = 11$, identify which integers in the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ are primitive roots modulo 11 and find their sum. | [
{
"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_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": "9",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the vertical addition on the right, the same Chinese characters represent the same digits from 1 to 9, while different Chinese characters represent different digits. How many two-digit numbers can be represented by '数学' in the vertical addition shown below?
$$
\begin{array}{r}
\text { 学习 } \\
\text { 学习 } \\
+ \text... | [
{
"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": "\\frac{311}{648}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Six standard six-sided dice are rolled. We are told there is no four-of-a-kind, but there is a pair of dice that show the same number. These two dice are set aside, and the other four dice are re-rolled. What is the probability that after re-rolling these four dice, at least four of the six dice show the same value? | [
{
"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{311}{648} |
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": "\\begin{pmatrix} 8 & 0 \\\\ 0 & 8 \\end{pmatrix}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let matrix $\mathbf{A}$ be an invertible matrix such that $(\mathbf{A} - 3 \mathbf{I})(\mathbf{A} - 5 \mathbf{I}) = \mathbf{0}.$ Calculate the value of $\mathbf{A} + 15 \mathbf{A}^{-1}.$ | [
{
"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... | \begin{pmatrix} 8 & 0 \\ 0 & 8 \end{pmatrix} |
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": "2493",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the smallest positive four-digit number divisible by 9 which has two even and two odd digits, with the thousands digit being at least 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... | 2493 |
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}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A manager schedules an informal review at a café with two of his team leads. He forgets to communicate a specific time, resulting in all parties arriving randomly between 2:00 and 4:30 p.m. The manager will wait for both team leads, but only if at least one has arrived before him or arrives within 30 minutes after him.... | [
{
"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_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": "\\left( 2, \\frac{7\\pi}{4} \\right)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Convert the point $(\sqrt{2}, -\sqrt{2})$ in rectangular coordinates to polar coordinates. Enter your answer in the form $(r,\theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$ | [
{
"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( 2, \frac{7\pi}{4} \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": "1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the line $3x-2y=0$ and the circle $(x-m)^{2}+y^{2}=1$ intersect, find the value of the positive integer $m$. | [
{
"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... | 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}{24}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x)=\begin{cases} (\frac{1}{2})^{x} & x\geqslant 4 \\ f(x+1) & x < 4 \end{cases}$, find the value of $f(2+\log_{2}3)$. | [
{
"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}{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": "13",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If a three-digit number $n=\overline{abc}$ is a perfect square, and the sum of its digits $a+b+c$ is also a perfect square, then $n$ is called a "super square number." Find the number of such super square numbers. | [
{
"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... | 13 |
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": "141",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Observe the following equations: $(x^2+x+1)^0=1$; $(x^2+x+1)^1=x^2+x+1$; $(x^2+x+1)^2=x^4+2x^3+3x^2+2x+1$; $(x^2+x+1)^3=x^6+3x^5+6x^4+7x^3+6x^2+3x+1$; ...; It can be inferred that in the expansion of $(x^2+x+1)^5$, the sum of the coefficients of the fifth, sixth, and seventh terms is $\boxed{141}$. | [
{
"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... | 141 |
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 + y + 2 = 0",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the curves $C_1: y = -x^2 + 4x - 2$, $C_2: y^2 = x$, if $C_1$ and $C_2$ are symmetric about the line $l$, then find the equation of $l$. | [
{
"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 + y + 2 = 0 |
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": "-2011",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given \(a^{2}(b+c)=b^{2}(a+c)=2011\) and \(a \neq b\), find the value of \(abc\). | [
{
"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... | -2011 |
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 $$\frac {a+2i}{i}=b+i$$ (where $a$, $b$ are real numbers) and $i$ is the imaginary unit, find $a+b=$ \_\_\_\_\_. | [
{
"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... | 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": "193",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \( a \) and \( b \) be positive integers such that \( 79 \mid (a + 77b) \) and \( 77 \mid (a + 79b) \). Find the smallest possible value of \( a + b \). | [
{
"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... | 193 |
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"
} | Define a new operation: $a*b=a^{b}-b^{a}$. Calculate the value of $(3*2)*4$. | [
{
"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... | -3 |
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