
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
In a regular pyramid \( PABC \), the side of the base \( ABC \) is equal to \( a \), and the lateral edge is \( 2a \). Points \( P, B \), and \( C \) lie on the lateral surface of a cone with vertex at point \( A \). Find the angle at the vertex of the axial cross-section of the cone.

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