
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 constructed using the height of a cone as its diameter. The surface area of the part of the sphere lying inside the cone is equal to the surface area of the part of the cone lying inside the sphere. Find the angle in the axial section of the cone.

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