
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
A sphere is inscribed in a cone, and the surface area of the sphere is equal to the area of the base of the cone. Find the cosine of the angle at the vertex in the axial section of the cone.

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