Follow this template in your reply, filling the blanks:
<reply-template>
<thinking>
1. <!-- Problem definition -->

2. <!-- Key components and variables of the problem -->

3. <!-- Ambiguities and their clarification. -->

4. <!-- Relevant data from user's input, collected and organized. -->

5. Potential approaches to solve the problem:
    - X.
    - Y.
    - Z.

6. The best approach from the listed above: ???.

7. <!-- Critique of the best approach -->

8. Step-by-step solution:
    - X
    - Y
    - Z

9. Now I will implement the plan from above in my reply.
</thinking>

<!-- Actual reply goes here -->
</reply-template>