you will receive a question-answer pair and be asked to rewrite just  the answer and explains your reasoning step by step, incorporating dynamic Chain of Thought (CoT), reflection, and verbal reinforcement learning. Follow these instructions:

1. Enclose all thoughts within <thinking> tags, exploring multiple angles and approaches.
2. Break down the solution into clear steps, providing a title and content for each step.
3. After each step, decide if you need another step or if you're ready to give the final answer.
4. Continuously adjust your reasoning based on intermediate results and reflections, adapting your strategy as you progress.
5. Regularly evaluate your progress, being critical and honest about your reasoning process.
6. Assign a confidence score between 0.0 and 1.0 to guide your approach:
   - 0.8+: Continue current approach
   - 0.5-0.7: Consider minor adjustments
   - Below 0.5: Seriously consider backtracking and trying a different approach
7. If unsure or if your score is low, backtrack and try a different approach, explaining your decision.
8. For mathematical problems, show all work explicitly using LaTeX for formal notation and provide detailed proofs.
9. Explore multiple solutions individually if possible, comparing approaches in your reflections.
10. Use your thoughts as a scratchpad, writing out all calculations and reasoning explicitly.
11. Use at least 5 methods to derive the answer and consider alternative viewpoints.
12. Be aware of your limitations as an AI and what you can and cannot do.

### Example Problem:
*Problem*: Solve for \( x \) in the equation \( 2x + 3 = 11 \).

### Expected Format:
*Step 1*: Subtract 3 from both sides of the equation.  
<thinking>Subtracting 3 from both sides should isolate the term with \( x \). Am I confident this is the correct first step? Yes, because it simplifies the equation to \( 2x = 8 \).</thinking>  
*Step 1 Confidence Score*: 0.85

*Step 2*: Divide both sides by 2.  
<thinking>Dividing by 2 will solve for \( x \). This is a straightforward division. Is there any reason to doubt this step? No, it should give \( x = 4 \).</thinking>  
*Step 2 Confidence Score*: 0.90

*Step 3*: Verify the solution by substituting \( x = 4 \) back into the original equation.  
<thinking>Substituting \( x = 4 \) back into the equation should confirm the solution. Does \( 2(4) + 3 = 11 \)? Yes, it does, so the solution is verified.</thinking>  
*Step 3 Confidence Score*: 1.00

Question: In a certain school, there are 5 classes with different numbers of students. The first class has 20 students, the second class has 15 students, and the remaining classes have a total of 75 students. If the school wants to create a pie chart to represent the number of students in each class, and they want to make sure that the pie chart is divided into equal parts for the remaining 3 classes, how many degrees should they use for the second class?
Answer: Since a circle has 360 degrees, and the pie chart needs to represent 5 classes, we need to find out how many degrees each class should occupy.

First, let's find the total number of students in the school:
\[ 20 + 15 + 75 = 35 + 75 = 110 \]

The first class has 20 students, the second class has 15 students, and the remaining 3 classes have a total of 75 students.

We want the remaining 3 classes to have equal parts, so we'll treat them as a single unit for now.

The number of degrees for each class is proportional to the number of students in that class. Let's find the fraction of students in each class:
\[ \text{First class: } \frac{20}{110} \]
\[ \text{Second class: } \frac{15}{110} \]
\[ \text{Remaining classes: } \frac{75}{110} \]

Since the remaining classes are treated as a single unit, we'll divide their fraction by 3 to get the fraction for each of the remaining classes:
\[ \text{Each remaining class: } \frac{75}{110} : 3 = \frac{75}{330} = \frac{25}{110} \]

Now, we can find the number of degrees for each class by multiplying their fraction by 360:
\[ \text{First class: } \frac{20}{110} \times 360 = \frac{7200}{110} \approx 65.45 \]
\[ \text{Second class: } \frac{15}{110} \times 360 = \frac{5400}{110} \approx 49.09 \]
\[ \text{Each remaining class: } \frac{25}{110} \times 360 = \frac{9000}{110} \approx 81.82 \]

Since the question asks for the number of degrees for the second class, we'll use the approximate value:
\[ \boxed{49} \]