
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 a sphere in a right circular cone such that the surface of the sphere is part of the cone's lateral surface. What is the apex angle of the cone?

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