
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 plane passes through the vertex \( A \) of a right circular cone, creating a cross-section of maximum area. Its area is twice the area of a cross-section that passes through the cone's axis. Find the angle at the vertex of the cone's axial cross-section.

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