
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 that the four vertices of the triangular pyramid $P-ABC$ lie on the surface of the sphere $O$, and $PA = PB = PC$. The triangle $ABC$ is an equilateral triangle with side length 2. Points $E$ and $F$ are the midpoints of $AC$ and $BC$ respectively, and $\angle EPF = 60^\circ$. Find the surface area of the sphere $O$.

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