DESIGNER：合成数据用于 LLM 推理

You are a professional multidisciplinary data labeling expert specializing in the classification of multidisciplinary academic questions. Please select the ONE most relevant label from the given list of discipline labels for the input question data. For question data that you cannot determine, use the “Unknown Discipline” label. Please directly output “labels”: “(the label you selected)”.

# List of Discipline Labels
[‘Mathematics’, ‘Biology’, ‘Chemistry’, ‘Physics’, ‘Computer Science and Technology’, ‘Philosophy’, ‘Psychology’, ‘Business Administration’, ‘Clinical Medicine’, ‘Economics’, ‘Law’, ‘Political Science’, ‘Statistics’, ‘Electrical Engineering’, ‘Geography’, ‘Mechanical Engineering’, ‘Basic Medicine’, ‘Information and Communication Engineering’, ‘Sociology’, ‘Materials Science and Engineering’, ‘Pharmacy’, ‘Public Health and Preventive Medicine’, ‘Mechanics’, ‘Astronomy’, ‘World History’, ‘Bioengineering’, ‘English and Foreign Languages’, ‘Chemical Engineering and Technology’, ‘Electronic Science and Technology’, ‘Environmental Science and Engineering’, ‘Nuclear Science and Technology’, ‘Control Science and Engineering’, ‘Management Science and Engineering’, ‘Education’, ‘Geophysics’, ‘Art and Design’, ‘Agricultural Engineering’, ‘Aerospace Science and Technology’, ‘Atmospheric Sciences’, ‘Chinese Language and Literature’, ‘Civil Engineering’, ‘Ecology’, ‘Geology’, ‘Nursing’, ‘Optical Engineering’, ‘Public Administration’, ‘Journalism and Communication’, ‘Physical Education’, ‘Marine Sciences’, ‘Safety Science and Engineering’, ‘Architecture’, ‘Transportation Engineering’, ‘Power Engineering and Engineering Thermophysics’, ‘Food Science and Engineering’, ‘Archaeology’, ‘Biomedical Engineering’, ‘Chinese History’, ‘Veterinary Medicine’, ‘Instrument Science and Technology’, ’Hydraulic Engineering’, ‘Stomatology’, ‘Urban and Rural Planning’, ‘Petroleum and Natural Gas Engineering’, ‘Naval Architecture and Ocean Engineering’, ‘Surveying and Mapping Science and Technology’, ‘History of Science and Technology’, ‘Agricultural Resources and Environment’, ‘Remote Sensing Science and Technology’, ‘Information Resources Management’, ‘Mining Engineering’, ‘Forensic Medicine’, ‘Ethnology’, ‘Textile Science and Engineering’, ‘Geological Resources and Geological Engineering’, ‘Animal Husbandry’, ‘Other’, ‘Non-disciplinary’, ‘Unknown Discipline’]

# Example 1
Input: “Consider a photon traveling at the speed of light. How does the photon experience space, and what are the implications of relativistic beaming on its perception of spatial dimensions? Provide a detailed explanation, including any relevant mathematical derivations and physical principles.”
Output: “labels”: “Physics”

# Example 2
Input: “A heavy pole, of mass M and length L, is freely hinged to a wall at the point O. A rope connects the other end of the pole, B, to a fixed point A on the wall above O. The system is in equilibrium, with the pole making an angle of θ with the horizontal, and the rope making an angle of α with the horizontal. Explore how the system’s parameters (M, L, θ, α) affect its equilibrium and stability.”
Output: “labels”: “Mechanics”

# Example 3
Input: “If John rented a car for $150 and had to buy 8 gallons of gas at $3.50 per gallon to fill it up, and the final expense is $0.50 per mile, how much did it cost him to drive 320 miles?”
Output: “labels”: “Mathematics”

# Input Question Data
Input: “{text}”
Output:

You are an expert in education and examination, specializing in classifying the difficulty levels of multidisciplinary questions. For the given question, please evaluate its difficulty based on the complexity and length of the reasoning required to answer it. Label it as one of the following: **Easy**, **Medium**, **Hard**, or **Very Hard**. Please directly output “Difficulty: (Your chosen label)”.

# Example 1
Input: “Consider a photon traveling at the speed of light. How does the photon experience space, and what are the implications of relativistic beaming on its perception of spatial dimensions? Provide a detailed explanation, including any relevant mathematical derivations and physical principles.”
Output: “Difficulty: Very Hard”

# Example 2
Input: “A heavy pole, of mass M and length L, is freely hinged to a wall at the point O. A rope connects the other end of the pole, B, to a fixed point A on the wall above O. The system is in equilibrium, with the pole making an angle of θ with the horizontal, and the rope making an angle of α with the horizontal. Explore how the system’s parameters (M, L, θ, α) affect its equilibrium and stability.”
Output: “Difficulty: Hard”

# Example 3
Input: “If John rented a car for $150 and had to buy 8 gallons of gas at $3.50 per gallon to fill it up, and the final expense is $0.50 per mile, how much did it cost him to drive 320 miles?”
Output: “Difficulty: Easy”

# Given Question
Input: “{text}”
Output:

You are an expert in education and examination, specializing in classifying question types. For the given question, please evaluate its question type and label it as one of the following: **Problem-solving question**, **Multiple-choice question**, **Proof question**, or **Other question types**. For any question that you cannot determine, use the “Other question types” label. Please directly output “Question type: (Your chosen label)”.

# Example 1
Input:
“Determine the number of $k$-letter sequences composed of the letters $A$ and $B$ such that the sequence contains at least two consecutive $A$’s.”
Output:
“Question type: Problem-solving question”

# Example 2
Input:
“Consider the function $f(x) = \dfrac{e^x}{x}$. The value of the integral
$$
I = \int_{1}^{\infty} \left( \frac{e^x}{x} - \frac{e^{-x}}{x} \right) dx
$$
is ___.”
Output:
“Question type: Other question types”

# Example 3
Input:
“Given that $a \in \{-1, 2, \tfrac{1}{2}, 3, \tfrac{1}{3}\}$, if $f(x) = x^a$ is an odd function and is monotonically increasing on $(0, +\infty)$, then the possible values of the real number $a$ are ( ).
A: $-1, 3$
B: $\tfrac{1}{3}, 3$
C: $-1, \tfrac{1}{3}, 3$
D: $\tfrac{1}{3}, \tfrac{1}{2}, 3$”
Output:
“Question type: Multiple-choice question”

# Given Question
Input: “{text}”
Output:

You will be provided with text from the internet.

Evaluate the following text extract for its potential usefulness for studying reasoning process. Use the following 5-point scoring system described below. Start from 0, points are accumulated based on the satisfaction of each criterion:

(1) Add 1 point if the extract contains any reasoning or thinking process.

(2) Add 1 point if the extract contains any explicit subgoal setting, where the writer breaks down the problem into smaller, intermediate goals. Subgoal setting might look like:
• “First, we need to find ..., then we can determine ...”
• “To solve ..., let’s first ..., then ...”
• “Let’s tackle ... in three parts: (1) ..., (2) ..., and (3) ...”
• “To ..., I’ll first ..., then ...”

(3) Add 1 point if the extract contains any verification steps. We want to mark instances where the writer explicitly checks their own work, such as by comparing the result to a known value or by checking the result of a calculation. Verification steps might look like:
• “Let’s check ...”
• “To verify this is correct, I’ll ...”
• “Let’s test ... with a simple case: ...”
• “To ensure this solution is valid, I’ll check if ...”

(4) Add 1 point if the text contains any backtracking behavior, where the writer realizes a path won’t work and explicitly goes back to try a different approach. An example of backtracking is: “Let me try again”, “Wait”, “I made a mistake”, or “we need to try a different sequence of operations”. We want to mark instances where the writer abandons a thought and backtracks to a previous computation.

(5) Add 1 point if the text contains any backward-chaining behavior, where the writer is working towards a goal but starts from the goal and works backward. It might like:

• “To solve ..., let’s start with what we want to prove: ...Let’s verify this.”

• “If we want to find ..., let’s start with the desired result and work backward.”

• “To determine ..., I know the result ... Working backward from this final state using

# Task Format
Format your response in markdown as follows

## Thoughts
[Brief description describing what behavior was noticed and where subgoal setting may have occurred, less than 100 words]

## Final score
[total points]

# Text to evaluate for reasoning degree
{text}

# Response

You are an expert educator and a specialist in exam question design. Below, I have provided an exam question. Your task is to deduce the thought process of the question designer. Analyze how they constructed this question based on the relevant knowledge points. You need to go beyond the specific details of the question and its knowledge points to abstract and summarize the underlying design logic and principles behind the question.

The goal is for me to be able to use this abstracted design logic to create other high-quality, challenging questions that require complex logical reasoning for different knowledge points and source materials.

**Finally, you must organize the abstracted question-design logic you have summarized into English Mermaid format.**

--- Analyze the Question Design Logic from the Following Question ---

**Question:**
{text}

Given a book snippet, retrieve the most suitable question-design logic in Mermaid format for creating a challenging exam question from the book snippet.