
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
We inscribe triangle \(ABC\) in a circle with radius \(r\). The triangle is rotated around the tangent drawn at the fixed point \(A\). Under what position of side \(BC\) will the surface area generated by the rotation of \(BC\) be the largest?

Present the answer in LaTex format: \boxed{Your answer}
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