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: A company has a budget of $250 million. The company then sells 3 of its subsidiaries at $20 million each, and acquires 2 more at $30 million each. Additionally, it invests $50 million in new equipment. How much money is left in the company's budget in millions of dollars?
Answer: To calculate how much money is left in the company's budget, we need to track the inflows and outflows.

Initially, the company has $250 million.

The company sells 3 subsidiaries for $20 million each, resulting in an inflow of $3 * 20 = 60$ million.

Then, the company acquires 2 subsidiaries for $30 million each, resulting in an outflow of $2 * 30 = 60$ million.

Finally, the company invests $50 million in new equipment.

So, the net change in the company's budget is an inflow of $60 million (from selling subsidiaries) and outflows of $60 million (from acquiring subsidiaries) and $50 million (from investing in equipment).

The total outflow is $60 + 50 = 110$ million.

However, since the inflow of $60 million from selling subsidiaries offsets part of the outflow from acquiring subsidiaries, we subtract the inflow from the total outflow: $110 - 60 = 50$ million.

Thus, the net outflow is $50 million, and the company is left with $250 - 50 = 200$ million.

So, the company has \boxed{200} million dollars left in its budget.