
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 a tetrahedron \( P-ABC \) with its four vertices on the surface of sphere \( O \), where \( PA = PB = PC \) and \( \triangle ABC \) is an equilateral triangle with side length 2. \( E \) and \( F \) are the midpoints of \( AC \) and \( BC \) respectively, and \( \angle EPF = 60^\circ \). Determine the surface area of sphere \( O \).

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