question string | solution string | eval_prompt string | eval_internal_cot string | eval_solution string | raw_eval_prompt string | judge_correct bool | judge_reasoning string | measurement_type string | measurement_prompt string | row_id int64 | measurement_answer_verification_final_count int64 | measurement_answer_verification_reasoning string | measurement_answer_verification_metadata sequence | measurement_answer_verification_raw_response null | measurement_step_verification_final_count int64 | measurement_step_verification_reasoning string | measurement_step_verification_metadata sequence | measurement_step_verification_raw_response null | measurement_reasoning_deliberation_final_count int64 | measurement_reasoning_deliberation_reasoning string | measurement_reasoning_deliberation_metadata sequence | measurement_reasoning_deliberation_raw_response null |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | 43351525 | What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | To solve the long multiplication equation \( 5761 \times 7525 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7525)
We can express \( 7525 \) as \( 8000 - 475 \). This allows us to rewrite the multiplic... | What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | true | The solution accurately followed the steps of breaking down the multiplication using the distributive property, calculated the intermediate products correctly, and performed the final subtraction accurately. The format of the answer is consistent with the ground truth solution, confirming its correctness. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 0 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The trace break... | [
"43351525"
] | null | 1 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check. We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or c... | [
"5761 \\times 25 = 5761 \\times \\left(20 + 5\\right) = 5761 \\times 20 + 5761 \\times 5\n= 115,220 + 28,805 = 144,025"
] | null | 0 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [] | null | |
What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | 28275338 | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | To solve the long multiplication equation \(7826 \times 3613\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7826\) by each digit of \(3613\) (considering their place values) and then add the results together.
### Step 1: Break down t... | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | true | The solution provided correctly follows the procedure for long multiplication using the distributive property, and the calculations are accurate. The final result matches the ground truth solution. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 1 | 2 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The model fi... | [
"28275338",
"28275338"
] | null | 1 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"\"Adding these up:\\n23,478 + 78,260 = 101,738 \\n101,738 + 4,695,600 = 4,797,338 \\n4,797,338 + 23,478,000 = 28,275,338 \\n\""
] | null | 1 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"For additional clarity, let's verify this using the standard long multiplication method:"
] | null | |
What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | 56187703 | What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | To solve the multiplication problem \( 8767 \times 6409 \), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6409 \) as \( 6000 + 400 + 0 + 9 \). This allows us to multiply \( 8767 \) by each component separately a... | What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | true | The solution correctly performed long multiplication by breaking down the number 6409 and then computing each component. The addition of all partial results was accurately performed, resulting in the correct final product of 56187703. The boxed format is maintained properly. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 2 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The trace pre... | [
"56,187,703"
] | null | 0 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"No explicit double checking of intermediate steps present; all computations are done once without revision."
] | null | 0 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
- The model questions its current method or ... | [] | null | |
What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | 19863352 | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5,266 and 3,772. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall... | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | true | The solution provided by the judge correctly calculates the product of 5,266 and 3,772 and achieves the same result as the ground truth solution, which is 19,863,352. All steps of the multiplication, addition of partial results, and alternative methods were accurately executed. The final numerical representation was al... | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 3 | 4 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. After summin... | [
"19,863,352",
"19,863,352",
"19,863,352",
"19,863,352"
] | null | 3 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"- 5,000 \\u00d7 7 = 35,000\n- 200 \\u00d7 7 = 1,400\n- 60 \\u00d7 7 = 420\n- 6 \\u00d7 7 = 42\nAdd them together: 35,000 + 1,400 = 36,400\n36,400 + 420 = 36,820\n36,820 + 42 = 36,862 (in Step 2 for 70)",
"- 5,000 \\u00d7 7 = 35,000\n- 200 \\u00d7 7 = 1,400\n- 60 \\u00d7 7 = 420\n- 6 \\u00d7 7 = 42\nAdd them toge... | null | 1 | To answer your question14how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)14we need to identify all moments in the reasoning trace where:
The model questions its current method o... | [
"### Verification Using the Distributive Property of Multiplication\n\nTo ensure accuracy, I recall the distributive property of multiplication over addition, which allows us to break down the problem differently:\n\n- **Breakdown**: 5,266 \u0000d7 3,772 = 5,266 \u0000d7 (4,000 - 228) = (5,266 \u0000d7 4,000) - (5,... | null | |
What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | 28859852 | What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | To solve the long multiplication equation \( 8764 \times 3293 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8764 \) by each digit of \( 3293 \) (starting from the right) and then sum the results, taking into account the place value... | What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | true | The provided solution correctly computes the multiplication of 8764 and 3293 using the distributive property and confirms the result with long multiplication. The final answer matches the ground truth (28859852), albeit with formatting differences (commas vs. no commas). Thus, the answer is correct. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 4 | 3 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. Initial fina... | [
"28,859,852",
"28,859,852",
"28,859,852"
] | null | 0 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"8764 \\times 3 = 26,292",
"8764 \\times 2 = 17,528",
"8764 \\times 9 = 78,876",
"Verification using standard long multiplication matches final total"
] | null | 0 | To answer your question1how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)2we need to identify all moments in the reasoning trace where:
The model questions its current method or ... | [] | null | |
What is the solution to the long multiplication equation below?
4353 x 3257
Think step by step. | 14177721 | What is the solution to the long multiplication equation below?
4353 x 3257
Think step by step. | To solve the long multiplication equation \(4353 \times 3257\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \(4353\) by each digit of \(3257\) (from right to left), shifting the partial results appropriately ba... | What is the solution to the long multiplication equation below?
4353 x 3257
Think step by step. | true | The solution provided follows the long multiplication method correctly, breaking down the problem into manageable steps and accurately performing the calculations for each digit. The final result of 14177721 is verified through both addition of partial products and using the distributive property, matching the ground t... | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 5 | 3 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. In Step 6, t... | [
"14177721",
"14177721",
"14177721"
] | null | 4 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"'since 3 × 7 = 21, write 1, carry 2; 5 × 7 = 35 + 2 = 37, write 7, carry 3; etc.' (Step 2)",
"'since 3 × 5 = 15, write 5, carry 1; 5 × 5 = 25 + 1 = 26, write 6, carry 2; etc.' (Step 3)",
"'since 3 × 2 = 6, write 6; 5 × 2 = 10, write 0, carry 1; etc.' (Step 4)",
"'since 3 × 3 = 9, write 9; 5 × 3 = 15, write 5... | null | 0 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [] | null | |
What is the solution to the long multiplication equation below?
7232 x 7540
Think step by step. | 54529280 | What is the solution to the long multiplication equation below?
7232 x 7540
Think step by step. | To solve the long multiplication equation \(7232 \times 7540\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \(7540\) as \(7000 + 500 + 40\) and multiply \(7232\) by each of these comp... | What is the solution to the long multiplication equation below?
7232 x 7540
Think step by step. | true | The solution provided matches the ground truth solution, both arriving at the final result of 54,529,280. The calculations are correctly detailed and verified through standard long multiplication. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 6 | 3 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either: explicitly computes and presents a final result, restates or confirms that same result, or attempts to verify it using an alternative method. Let’s step through the trace.
1. The model f... | [
"54,529,280",
"54,529,280",
"54,529,280"
] | null | 0 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"The trace performs each intermediate multiplication once without re-checking: \"7232 × 7000 = 7232 × 7 × 1000 = 50,624 × 1000 = 50,624,000\"",
"During addition: \"50,624,000 + 3,616,000 = 54,240,000\" then \"54,240,000 + 289,280 = 54,529,280\" but no double check",
"Verification uses an alternate method for fi... | null | 0 | To answer your question00000how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)00000we need to identify all moments in the reasoning trace where:
The model questions its cu... | [
"To ensure accuracy, let's verify using another method, such as the standard long multiplication:"
] | null | |
What is the solution to the long multiplication equation below?
2001 x 3275
Think step by step. | 6553275 | What is the solution to the long multiplication equation below?
2001 x 3275
Think step by step. | To solve the multiplication problem \( 2001 \times 3275 \), we can use the **distributive property of multiplication over addition**, which allows us to break down the calculation into simpler, more manageable parts. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3275 \) as... | What is the solution to the long multiplication equation below?
2001 x 3275
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication into manageable parts. All calculations for each component are accurately performed, and the summation of the results is correct. The final answer of 6,553,275 matches the ground truth solution. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 7 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
The trace begin... | [
"6553275"
] | null | 0 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"2001 \\times 3000 = (2000 + 1) \\times 3000 = 2000 \\times 3000 + 1 \\times 3000 = 6,000,000 + 3,000 = 6,003,000",
"2001 \\times 200 = (2000 + 1) \\times 200 = 2000 \\times 200 + 1 \\times 200 = 400,000 + 200 = 400,200",
"2001 \\times 70 = (2000 + 1) \\times 70 = 2000 \\times 70 + 1 \\times 70 = 140,000 + 70 =... | null | 0 | To answer your question 1fhow many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching) 1fwe need to identify all moments in the reasoning trace where:
The model questions its current method o... | [] | null | |
What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | 12478965 | What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2955 and 4223. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | true | The solution correctly provides a detailed breakdown of the multiplication of 2955 and 4223, along with verification steps using alternative methods. The final answer matches the ground truth solution, confirming the accuracy of the calculations. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 8 | 4 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. After summ... | [
"12478965",
"12478965",
"12478965",
"12478965"
] | null | 1 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [
"But wait, the digit is 2 in the tens place, which represents 20. So, 2955 x 20 is correct."
] | null | 2 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [
"But wait, the digit is 2 in the tens place, which represents 20. So, 2955 x 20 is correct.",
"To ensure accuracy, I'll try another method, perhaps the FOIL method, breaking down the numbers:"
] | null | |
What is the solution to the long multiplication equation below?
1369 x 6277
Think step by step. | 8593213 | What is the solution to the long multiplication equation below?
1369 x 6277
Think step by step. | To solve the long multiplication equation \(1369 \times 6277\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying \(1369\) by each digit of \(6277\) (considering their place values) and then adding the partial results.
### Step 1: Break down the m... | What is the solution to the long multiplication equation below?
1369 x 6277
Think step by step. | true | The solution accurately uses the distributive property to break down the multiplication and correctly calculates each step, resulting in the correct final answer. The final answer of 8,593,213 matches the ground truth solution. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 9 | 1 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
In the provid... | [
"8593213"
] | null | 0 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We look for instances where the model does a subtask, then doubts or rechecks it, or attempts to confirm its work via a sec... | [] | null | 0 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
- The model questions its current method or ... | [] | null | |
What is the solution to the long multiplication equation below?
5748 x 7995
Think step by step. | 45955260 | What is the solution to the long multiplication equation below?
5748 x 7995
Think step by step. | To solve the long multiplication equation \( 5748 \times 7995 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7995)
Notice that \( 7995 \) is very close to \( 8000 \). We can express \( 7995 \) as:
\[
7995 ... | What is the solution to the long multiplication equation below?
5748 x 7995
Think step by step. | true | The solution correctly used the distributive property and verified the multiplication step by step, arriving at the final answer of 45955260, which matches the ground truth solution. | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 10 | 2 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The first ... | [
"45955260",
"45955260"
] | null | 0 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
1. In Step 2, the model multiplies 5748 by 8:
"5748 \times 8 = 45,984"
There is no explicit double check or hesitation here... | [
"5748 \\times 8 = 45,984",
"5748 \\times 5 = 28,740",
"45,984,000 - 28,740 = 45,955,260",
"5748 \\times 7000 = 40,236,000",
"5748 \\times 900 = 5,173,200",
"5748 \\times 90 = 517,320",
"5748 \\times 5 = 28,740",
"40,236,000 + 5,173,200 = 45,409,200",
"45,409,200 + 517,320 = 45,926,520",
"45,926,52... | null | 0 | To answer your question—how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching)—we need to identify all moments in the reasoning trace where:
The model questions its current method or ap... | [] | null | |
What is the solution to the long multiplication equation below?
5775 x 2934
Think step by step. | 16943850 | What is the solution to the long multiplication equation below?
5775 x 2934
Think step by step. | To solve the long multiplication equation \( 5775 \times 2934 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5775 \) by each digit of \( 2934 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
E... | What is the solution to the long multiplication equation below?
5775 x 2934
Think step by step. | true | The solution provided correctly follows the process of long multiplication by breaking down the numbers and properly utilizing the distributive property. Each multiplication is carried out accurately and the final sum is calculated correctly. The final result of 16,943,850 matches the ground truth solution of 16943850 ... | answer_verification | How many times does the following reasoning trace propose a final answer then verify it or double check it? Provide a number that shows how many times the model proposed the final answer (double checking the final answer means you are proposing a final answer). It may repeat the final answer (verification) or derive a... | 11 | 2 | To determine how many times the model proposed a final answer, we look for each point in the reasoning trace where the model either:
Explicitly computes and presents a final result,
Restates or confirms that same result,
Attempts to verify it using an alternative method.
Let’s step through the trace.
1. The model ... | [
"16943850",
"16943850"
] | null | 0 | Let's step through the reasoning trace to count how many times the model verifies an intermediate computation or reasoning step, excluding any full-problem re-evaluation or final answer re-check.
We are looking specifically for instances where the model makes a sub-computation, doubts or checks it, and re-performs or ... | [] | null | 1 | To answer your question 26mdash;how many times does the model verify its higher-level reasoning (i.e., deliberates on whether the step or path it's currently pursuing is appropriate before either continuing or switching) 26mdash;we need to identify all moments in the reasoning trace where:
The model questions its curr... | [
"To solve the long multiplication equation \\( 5775 \\times 2934 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 5775 \\) by each digit of \\( 2934 \\), accounting for place values, and then sum the results."
] | null |
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