data_source stringclasses 6
values | prompt listlengths 2 2 | ability stringclasses 1
value | reward_model dict | extra_info dict | problem stringlengths 21 4.23k | prompt_messages listlengths 2 2 | gt stringlengths 1 1.99k |
|---|---|---|---|---|---|---|---|
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 + 2i",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Determine the complex number $z$ satisfying the equation $(1+2i)z=-3+4i$. | [
{
"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 + 2i |
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 $x\in \mathbb{R}$, find the derivative of the function $f(x)=e^x - \ln 2$ and evaluate it at $x=0$. | [
{
"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... | 1 |
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": "4000",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $x$ be the number of students in Mina's high school. Given that Nina's high school has 5 times as many students as Mina's high school, the number of students in Nina's high school is $5x$. Furthermore, if 200 students were to transfer from Nina's high school to Mina's high school, the total number of students in Mi... | [
{
"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... | 4000 |
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": "0.95",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the probability of producing a Grade B product is $0.03$, and the probability of producing a Grade C product is $0.02$, calculate the probability of randomly inspecting a product and finding it to be a qualified product. | [
{
"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... | 0.95 |
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": "400",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In rectangle $ABCD$, $AB=BC=15$, $CD=DA=20$, and $\angle D=90^\circ$. Points $X$ and $Y$ are the midpoints of $\overline{BC}$ and $\overline{DA}$ respectively. Compute $XY^2$ (the square of the length of $XY$). | [
{
"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... | 400 |
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": "396",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the product of all positive integral values of \( n \) such that \( n^2 - 40n + 399 = p \) for some prime number \( p \). Note that there is at least one such \( n \). | [
{
"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... | 396 |
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": "-6a^{5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the result of $-2a^{3}\cdot 3a^{2}$. | [
{
"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... | -6a^{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": "-13",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $\left(1-x\right)^{5}(1-2x)^{4}=a_{0}+a_{1}x+a_{2}x^{2}+\cdots +a_{9}x^{9}$, then $a_{0}+a_{1}+a_{2}+\cdots +a_{9}=$____, $a_{1}=$____. | [
{
"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... | -13 |
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": "900",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the number of positive integers less than 1200 that are divisible by neither 6 nor 8. | [
{
"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... | 900 |
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": "5",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $x > 1$, find the minimum value of $x + \frac{4}{x - 1}$. | [
{
"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... | 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": "15",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the diagram, $\triangle ABC$ has angles that measure $60^{\circ}$, $(5x)^{\circ}$ and $(3x)^{\circ}$. 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... | 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": "a(b+3)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $\lg 2 = a$ and $\log_{2} 7 = b$, find $\lg 56$. | [
{
"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... | a(b+3) |
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, 1, 2, 6",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the last digit of the number \(1989^{1989}\)? What are the last digits of the numbers \(1989^{1992}\), \(1992^{1989}\), and \(1992^{1992}\)? | [
{
"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, 1, 2, 6 |
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{129}{1024}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A fair coin is flipped $10$ times. What is the probability that at least $6$ consecutive flips come up heads? | [
{
"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{129}{1024} |
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 {9}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given an arithmetic-geometric sequence {a_n} with the first term of 2 and a common ratio of $- \frac {1}{3}$. The sum of its first n terms is denoted as S_{n}. If for any n∈N*, there's always A≤3S_{n} - $\frac {1}{S_{n}}$≤B, find the minimum value of B-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 {9}{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": "10x^4 - 6x^3 + 35x^2 - 26x + 3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Expand the product $(5x-3)(2x^3 + 7x - 1)$. | [
{
"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... | 10x^4 - 6x^3 + 35x^2 - 26x + 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": "\\frac{3}{10}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | I randomly pick an integer $p$ between $1$ and $10$ inclusive. What is the probability that I choose a $p$ such that there exists an integer $q$ so that $p$ and $q$ satisfy the equation $pq - 5p - 3q = 1$? Express your answer as a common fraction. | [
{
"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}{10} |
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": "B) 1 : 30",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \( N = 18 \cdot 52 \cdot 75 \cdot 98 \). What is the ratio of the sum of the odd divisors of \( N \) to the sum of the even divisors of \( N \)?
A) 1 : 29
B) 1 : 30
C) 1 : 31
D) 1 : 32 | [
{
"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... | B) 1 : 30 |
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": "22",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Each of the numbers $b_1, b_2, \dots, b_{100}$ is $\pm 1.$ Find the smallest possible positive value of
\[\sum_{1 \le i < j \le 100} b_i b_j.\] | [
{
"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_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": "(7,3)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the vectors $\overrightarrow{a}=(3,5)$ and $\overrightarrow{b}=(-2,1)$ in the plane, calculate the value of $\overrightarrow{a}-2\overrightarrow{b}$. | [
{
"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... | (7,3) |
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": "3",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | How many perfect cubes are there between 100 and 500? | [
{
"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_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": "177",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \(\alpha, \beta\) be two distinct planes. Five points are taken in plane \(\alpha\), and seven points are taken in plane \(\beta\). Determine the maximum number of planes that can be determined by these points. | [
{
"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... | 177 |
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": "4\\sqrt{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In a right triangle $ABC$ with $AB$ as the hypotenuse, points $D$ and $E$ divide the hypotenuse into four equal lengths. If $AD = \tan(x)$ and $AE = \cot(x)$ for a real number $x$ such that $0 < x < \frac{\pi}{2}$, find the length of the hypotenuse $AB$. | [
{
"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... | 4\sqrt{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": "1980",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A graduating high school class has $45$ people. Each student writes a graduation message to every other student, with each pair writing only one message between them. How many graduation messages are written in total? (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... | 1980 |
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"
} | A cube is painted so that one side is blue, three sides are red, and two sides are green. How many different such cubes can be painted if all red sides must be visible from one vertex? | [
{
"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": "n \\cdot 2^{n+2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a sequence $\{a_n\}$ whose sum of the first $n$ terms is $S_n$, with $a_1 = 4$, and for every positive integer $n$, the following equation holds: $$\frac{1}{2} S_n - a_n + 2 = 0.$$
(1) Find the general term formula for the sequence $\{a_n\}$.
(2) Let $b_n = a_n \cdot \log_{\frac{1}{2}} \left(\frac{1}{a_n}\right)$... | [
{
"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... | n \cdot 2^{n+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": "20",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A school has a total of 300 teachers, among which there are 192 intermediate-level teachers. The ratio of the number of senior teachers to junior teachers is 5:4. To understand the professional development needs of teachers, stratified sampling method is used for the survey. In the extracted sample, there are 64 interm... | [
{
"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_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\\pi - 9",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Compute the exact value of the expression $\left|2\pi - | \pi - 9 | \right|$. Write your answer using only integers and $\pi$, without any absolute value signs. | [
{
"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\pi - 9 |
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"
} | In $\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. If $A=\dfrac{\pi}{3},a=\sqrt{3},b=1$, find the value of $c$. | [
{
"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_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": "(0,1)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the domain of the function $y=\ln (\frac{1}{x}-1)$. | [
{
"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... | (0,1) |
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": "n=12",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $S_{n}$ be the sum of the first $n$ terms of the sequence $\{a_{n}\}$, and it is known that $2S_n=3a_n-3(n∈N^*)$.
$(1)$ Find $a_{n}$;
$(2)$ If $b_n=\frac{1}{a_n}+log_3a_{2n-1}$, let $T_{n}$ be the sum of the first $n$ terms of $\{b_{n}\}$, and it satisfies $T_{n} \lt 150$, find the maximum 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... | n=12 |
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}{4}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In triangle $DEF$, $DE = 8$, $EF = 6$, and $FD = 10$.
[asy]
defaultpen(1);
pair D=(0,0), E=(0,6), F=(8,0);
draw(D--E--F--cycle);
label("\(D\)",D,SW);
label("\(E\)",E,N);
label("\(F\)",F,SE);
[/asy]
Point $Q$ is arbitrarily placed inside triangle $DEF$. What is the probability that $Q$ lies closer to $D$ than to ei... | [
{
"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}{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": "2.503",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A point \((4\sqrt{5}, d-2)\) is \(4d\) units away from the origin. What is the smallest possible value of \(d\)? | [
{
"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... | 2.503 |
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",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $\{a_n\}$ is a geometric sequence with $a_n > 0$, and $a_{2018}= \frac{\sqrt{2}}{2}$, find the minimum value of $\frac{1}{a_{2017}}+ \frac{2}{a_{2019}}$. | [
{
"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_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": "0.4821",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The user has three computer disks from companies $\mathrm{K}$, $\mathrm{L}$, and $\mathrm{M}$, one disk from each of these companies, but the company stamps on the disks are absent. Two out of the three disks are defective. What is the probability that the defective disks are from companies $\mathrm{L}$ and $\mathrm{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... | 0.4821 |
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 $f(x)= \begin{cases} x^{2}+4x+3, x\leqslant 0 \\ 3-x, x > 0 \end{cases}$, calculate the value of $f(f(5))$. | [
{
"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... | -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{4}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $\frac{a}{b}=\frac{1}{3}$, then $\frac{a+b}{b}=\_\_\_\_\_\_$. | [
{
"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{4}{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": "13.5\\sqrt{3} - \\frac{27\\pi}{8}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In a regular hexagon with a side length of 3, three semicircles are inscribed such that their diameters coincide with alternating sides of the hexagon. Calculate the area of the shaded region inside the hexagon but outside all of the semicircles. | [
{
"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... | 13.5\sqrt{3} - \frac{27\pi}{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": "\\frac {\\sqrt {5}}{2} \\leq e \\leq \\sqrt {5}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The hyperbola $\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$ (where $a > 1$ and $b > 0$) has a focal distance of $2c$. A straight line l passes through points $(a, 0)$ and $(0, b)$, and the sum of the distances from point $(1, 0)$ to line l and from point $(-1, 0)$ to line l is $s \geq \frac {4}{5}c$. Find the range... | [
{
"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 {5}}{2} \leq e \leq \sqrt {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": "126",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $(b_1,b_2,...,b_{10})$ be a permutation of $(1,2,3,...,10)$ where $b_1 > b_2 > b_3 > b_4 > b_5$ and $b_5 < b_6 < b_7 < b_8 < b_9 < b_{10}$.
Find the number of such permutations. | [
{
"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... | 126 |
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"
} | Given the function $f(x)=\log_{2}(|x+1|+|x-2|-m)$.
$(1)$ When $m=7$, find the domain of the function $f(x)$;
$(2)$ If the solution set of the inequality $f(x) \geqslant 2$ is $\mathbb{R}$, find the range of values for $m$. | [
{
"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... | (-\infty,-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{5}{6}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the area of the closed shape formed by the graph of the function $f(x) = \begin{cases} x^{2} & (0 \leq x \leq 1) \\ 2-x & (1 < x \leq 2)\end{cases}$ and the x-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... | \frac{5}{6} |
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": "341",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Compute $\sqrt{(20)(19)(18)(17)+1}$. | [
{
"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... | 341 |
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"
} | For the parabola $C: y^2 = 4x$, we say that points satisfying $y^2 < 4x$ are inside the parabola. If point $M(x, y_o)$ is inside $C$, then the line $l: yy_o = 2(x + x_o)$ and the parabola $C$ have $\boxed{0}$ common points. | [
{
"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_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": "\\$21",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A truck travels 240 miles using 5 gallons of diesel. How far can it travel with 7 gallons of diesel, and what would be the cost if diesel costs $3 per gallon? | [
{
"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": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the terminal side of angle $\theta$ passes through the point $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$, calculate the value of $\sin\theta$. | [
{
"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": "40",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A subset of the integers $1, 2, \ldots, 50$ has the property that none of its members is 4 times another. What is the largest number of members such a subset can 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... | 40 |
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": "\\sqrt{\\frac{a^2}{2} + ab + b^2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A right triangle \(ABC\) \((\angle A = 90^\circ)\) has two squares \(BEFC\) and \(AMNC\) positioned such that points \(E\) and \(A\) lie on opposite sides of line \(BC\), and points \(M\) and \(B\) lie on opposite sides of line \(AC\). Find the distance between the centers of the squares if \(AB = a\), \(AC = b\). | [
{
"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... | \sqrt{\frac{a^2}{2} + ab + b^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": "-2 \\text{ or } -1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | For circle $C_1$: $(x-m)^2+(y+2)^2=9$ and circle $C_2$: $(x+1)^2+(y-m)^2=4$ to be tangent internally, the value of $m$ 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... | -2 \text{ or } -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{5-\\sqrt{21}}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Solve the equation: $x^{2}-5x+1=0$ (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... | \frac{5-\sqrt{21}}{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": "-4",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If the pure imaginary number $z$ satisfies $(2-i)z=4-b(1+i)^2$ (where $i$ is the imaginary unit, and $b$ is a real number), solve for $b$. | [
{
"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... | -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": "\\begin{pmatrix} -4 & 16 \\\\ 10 & -13 \\end{pmatrix}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Compute \(\begin{pmatrix} 4 & -2 \\ -1 & 5 \end{pmatrix} \begin{pmatrix} 0 & 3 \\ 2 & -2 \end{pmatrix}\). | [
{
"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} -4 & 16 \\ 10 & -13 \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": "81",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In triangle $ABC$, $AB = 12$, $BC = 18$, and $CA = 22$. Let $D$ be a point in the interior of $\overline{BC}$. Let points $I_B$ and $I_C$ denote the incenters of triangles $ABD$ and $ACD$, respectively. The circumcircles of triangles $BI_BD$ and $CI_CD$ meet at distinct points $P$ and $D$. Find the maximum possible 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... | 81 |
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{\\sqrt{3}}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate the value of $\cos 390^{\circ}$. | [
{
"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{\sqrt{3}}{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": "x^3 - 12x^2 + 135",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $r_1$, $r_2$, and $r_3$ be the roots of the polynomial
\[ x^3 - 4x^2 + 5 = 0. \]
Find the monic polynomial, in $x$, whose roots are $3r_1$, $3r_2$, and $3r_3$. | [
{
"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... | x^3 - 12x^2 + 135 |
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{9(x - 2)^2}{16} - y^2 = 1 (y \\neq 0)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given two vertices of $\triangle ABC$ are $A(0,0)$ and $B(6,0)$, and vertex $C$ moves on the curve $\frac{x^2}{16} - \frac{y^2}{9} = 1$, find the trajectory equation of the centroid of $\triangle ABC$. | [
{
"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... | \frac{9(x - 2)^2}{16} - y^2 = 1 (y \neq 0) |
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, 9)",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Circle $S$ has its center at point $S(3, -4)$. Circle $S$ is reflected across the $x$-axis and then translated 5 units up. What are the coordinates of the image of the center of circle $S$? | [
{
"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... | (3, 9) |
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": "\\sqrt{39}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is $30^{\circ}$, $|\overrightarrow{a}|=\sqrt{3}$, and $|\overrightarrow{b}|=3$, calculate $|2\overrightarrow{a}+\overrightarrow{b}|$. | [
{
"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... | \sqrt{39} |
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": "1260",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | If $n = 2^{12} \cdot 3^{15} \cdot 5^{9}$, how many of the natural-number factors of $n$ are multiples of 360? | [
{
"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... | 1260 |
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": "7.5\\sqrt{3} - 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | On each side of a unit square, an equilateral triangle with side length 2 is constructed. At one end of each triangle, a new equilateral triangle of side length 1 is added. Another triangle of side length 1 is added at the opposite end of each initial triangle. Similar to the original, their interiors and the square’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... | 7.5\sqrt{3} - 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": "2.09",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In the tetrahedron \(EFGH\), it is given that \(EF = GH = 7\), \(EG = FH = 10\), and \(EH = FG = 11\). The points \(K, L, M, N\) are the centers of the circles inscribed in the triangles \(EFG\), \(EFH\), \(EGH\), and \(FGH\) respectively. Find the volume of the tetrahedron \(KLMN\). If necessary, round your answer to ... | [
{
"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... | 2.09 |
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}{2} < a \\leqslant \\frac{2}{3}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that $f(x)$ is an increasing function defined on $[-1,2)$, if $f(a-1) > f(1-3a)$, find the range of values for 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... | \frac{1}{2} < a \leqslant \frac{2}{3} |
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": "381654729",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Is there a number in which every digit from 1 to 9 is used exactly once, and for which the number formed by the first $k$ digits is divisible by $k$ for every $k$ from 1 to 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... | 381654729 |
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": "9996",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | What is the greatest possible four-digit number that is divisible by 6 and 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... | 9996 |
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"
} | Evaluate $\log_5\frac{1}{\sqrt{25}}$ and solve for $y$ in $5^y = 125$. | [
{
"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": "a_{6}=3a_{5}-2=3(3a_{4}-2)-2=3(3(3a_{3}-2)-2)-2=3(3(3(3a_{2}-2)-2)-2)-2=3(3(3(3(3a_{1}-2)-2)-2)-2)-2=3(3(3(3(3(1)-2)-2)-2)-2)-2=3(3(3(3(1)-2)-2)-2)-2=3(3(3(1)-2)-2)-2=3(3(1)-2)-2=3(1)-2=3-2=1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the sequence ${a_n}$ that satisfies $a_1=1$ and $a_{n+1}=3a_n-2$, find the value of $a_6$. | [
{
"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... | a_{6}=3a_{5}-2=3(3a_{4}-2)-2=3(3(3a_{3}-2)-2)-2=3(3(3(3a_{2}-2)-2)-2)-2=3(3(3(3(3a_{1}-2)-2)-2)-2)-2=3(3(3(3(3(1)-2)-2)-2)-2)-2=3(3(3(3(1)-2)-2)-2)-2=3(3(3(1)-2)-2)-2=3(3(1)-2)-2=3(1)-2=3-2=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": "②④",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Among the following propositions:
① All acute angles are equal;
② The perpendicular segment is the shortest;
③ Complementary angles are adjacent angles;
④ In the same plane, if $L_1 \perp L_2$ and $L_1 \perp L_3$, then $L_2 \parallel L_3$,
the true propositions are . (Fill in the correct serial 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... | 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": "1120",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the number of eight-digit numbers for which the product of the digits is equal to 16875. The answer should be an integer. | [
{
"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... | 1120 |
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{\\pi}{12}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Shift the graph of the function $y=\sin 2x$ to the left by $\varphi$ ($\varphi > 0$) units so that it coincides with the graph of the function $$y=\cos\left(2x- \frac{\pi}{3}\right)$$, then the minimum value of $\varphi$ 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... | \frac{\pi}{12} |
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": "14",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Compute: \(7 \cdot \frac{1}{17} \cdot 34.\) | [
{
"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_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": "d_n = 2^n - 1",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $f(x) = x-\tfrac1{x}$ , and defi ne $f^1(x) = f(x)$ and $f^n(x) = f(f^{n-1}(x))$ for $n\ge2$ . For each $n$ , there is a minimal degree $d_n$ such that there exist polynomials $p$ and $q$ with $f^n(x) = \tfrac{p(x)}{q(x)}$ and the degree of $q$ is equal to $d_n$ . Find $d_n$ . | [
{
"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... | d_n = 2^n - 1 |
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": "\\text{All families for which the equality holds are those where all subsets are of size } \\lfloor \\frac{n}{2} \\rfloor \\text{ or } \\lceil \\frac{n}{2} \\rceil.",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let $A$ be a family of subsets of $\{1,2,\ldots,n\}$ such that no member of $A$ is contained in another. Sperner’s Theorem states that $|A|\leq{n\choose{\lfloor\frac{n}{2}\rfloor}}$ . Find all the families for which the equality holds. | [
{
"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... | \text{All families for which the equality holds are those where all subsets are of size } \lfloor \frac{n}{2} \rfloor \text{ or } \lceil \frac{n}{2} \rceil. |
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}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the equations $3a - 2 = 1$ and $2b - 3a = 2$, find the value of $b$. | [
{
"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} |
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 {15}}{8}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given that $\cos C= \frac{1}{4}$ and $a^{2}=b^{2}+ \frac{1}{2}c^{2}$,
(I) find the value of $\sin (A-B)$;
(II) if $c= \sqrt {10}$, find the values 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{ \sqrt {15}}{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": "7",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \( N = 10^3 + 10^4 + 10^5 + 10^6 + 10^7 + 10^8 + 10^9 \). Calculate the sum of the digits 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... | 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": "\\left[0, \\dfrac{4}{3}\\right]",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given a point $P(x,y)$ satisfies $(x^2-8x+y^2-4y+16\leqslant 0)$, then the range of $\dfrac{y}{x}$ 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... | \left[0, \dfrac{4}{3}\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": "2160",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the coefficient of the $x^2$ term in the expansion of $(3x-2)^6$. | [
{
"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... | 2160 |
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": "53",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Find the greatest common divisor (GCD) of two integers 1908 and 4187. | [
{
"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... | 53 |
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"
} | Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that
\[f(x) f(y) - f(xy) = x^2 + y^2 - xy\]
for all real numbers $x$ and $y$. Find all possible values 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... | 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|-1≤slant x < 0, x∈R\\} \\text{ (or } [-1,0))",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the sets $A=\{x|x^{2}-2x > 0,x∈R\}$ and $B=\{x| \frac {x+1}{x-1}≤slant 0, x∈R\}$, 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... | \{x|-1≤slant x < 0, x∈R\} \text{ (or } [-1,0)) |
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": "\\frac{x-2}{x-1}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Calculate:<br/>$(1)(-1)^2+(-\frac{1}{3})^{-2}-|-5|+\left(3-\pi \right)^{0}$;<br/>$(2)\frac{x-2}{x^2-1}÷\frac{x+1}{x^2+2x+1}$. | [
{
"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{x-2}{x-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": "T_{n} = 2n^2 + 2n - 1 + \\left(\\frac{1}{2}\\right)^n",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given that the sequence $\{a_{n}\}$ is an arithmetic sequence with a positive common difference, and the sum of its first $n$ terms is ${S}_{n}={n}^{2}+n$; the sequence $\{b_{n}\}$, where all terms are positive, is a geometric sequence satisfying ${b}_{1}{b}_{3}=\frac{1}{16}$ and ${b}_{5}=\frac{1}{32}$.
$(1)$ Find th... | [
{
"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... | T_{n} = 2n^2 + 2n - 1 + \left(\frac{1}{2}\right)^n |
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"
} | For how many values of $a$ does the line $y = x + a$ pass through the vertex of the parabola $y = x^3 - 3ax + a^2$? | [
{
"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": "\\frac{4n-3}{6n-2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Let \( a_{1}, a_{2}, \cdots \) and \( b_{1}, b_{2}, \cdots \) be two arithmetic sequences, with their sums of the first \( n \) terms denoted as \( A_{n} \) and \( B_{n} \) respectively. It is known that for all \( n \in \mathbf{N} \),
$$
\frac{A_{n}}{B_{n}} = \frac{2n-1}{3n+1}.
$$
Determine the expression for \( \fra... | [
{
"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{4n-3}{6n-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": "\\frac{1}{2}",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | The length of the longer side of rectangle $R$ is $20\%$ more than the length of a side of square $S$. The length of the shorter side of rectangle $R$ is $20\%$ less than the length of a side of square $S$. Additionally, consider a right triangle $T$ formed with the sides of rectangle $R$ as its legs. What is the ratio... | [
{
"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": "b = -2",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | Given the function $f(x) = e^x(ax^2 + bx + 1)$, where $a, b \in \mathbb{R}$, and the derivative of $f(x)$ is denoted by $f'(x)$. It is also known that $f'(-1) = 0$.
(I) If $b = 1$, find the equation of the tangent to the curve $y = f(x)$ at the point $(0, f(0))$.
(II) If the minimum value of the function $f(x)$ on ... | [
{
"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... | b = -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": "333",
"style": "rule"
} | {
"index": 0,
"split": "dummy"
} | A \(20 \times 20 \times 20\) cube is divided into 8000 unit cubes. A number is written in each unit cube. In each row and each column of 20 small cubes, parallel to one of the edges of the cube, the sum of the numbers is 1. In one of the small cubes, the number written is 10. Three \(1 \times 20 \times 20\) layers pass... | [
{
"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... | 333 |
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"
} | Consider the function $g(x)$ defined on the interval $[-4, 4]$ as follows:
$$ g(x) = \begin{cases}
x^3 + x^2 - 2x & \text{if } -4 \leq x < 0 \\
2x - 4 & \text{if } 0 \leq x \leq 4
\end{cases} $$
How many values of $x$ satisfy $g(g(x)) = 3$? | [
{
"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... | 0 |
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