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 the language of Azura, there are 4 words: "zorvath", "tharros", "vyrak", and "lyraea". The only grammatical restriction is that "tharros" cannot immediately follow "vyrak". All other combinations are allowed, including repeated words. Determine the number of valid 4-word sentences in the language of Azura.
Answer: To find the number of valid 4-word sentences, we will first find the total number of possible sentences without any restrictions and then subtract the number of invalid sentences where "tharros" immediately follows "vyrak".

Total possible sentences without restrictions:
There are 4 options for each word in the sentence. Since we are forming 4-word sentences, the total number of possible sentences is:
\[ 4^4 = 256 \]

Now, let's count the number of invalid sentences where "tharros" immediately follows "vyrak". We consider the following cases:

1. "vyrak" is the first word, and "tharros" is the second word. The remaining two words can be any of the 4 words, so there are $4 \times 4 = 16$ invalid sentences in this case.

2. "vyrak" is the second word, and "tharros" is the third word. The first word can be any of the 4 words, and the last word can also be any of the 4 words, resulting in $4 \times 4 = 16$ invalid sentences in this case.

3. "vyrak" is the third word, and "tharros" is the fourth word. The first two words can be any of the 4 words, so there are $4 \times 4 = 16$ invalid sentences in this case.

Adding up the invalid sentences from all cases gives us:
\[ 16 + 16 + 16 = 32 + 16 = 48 \]

Finally, to find the number of valid sentences, we subtract the number of invalid sentences from the total possible sentences:
\[ 256 - 48 = \boxed{208} \]