
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
Given points A, B, and C on the surface of a sphere O with a radius of 2, and the angles formed by OA, OB, and OC are equal pairwise. When the volume of the triangular pyramid O-ABC is maximum, the area of the circular cross-section obtained by the plane ABC intersecting sphere O is \_\_\_\_\_\_.

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