
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 triangular pyramid $(P-ABC)$ that is inscribed in a sphere $(O)$, with $PA=PB=PC=2$, the sum of the areas of the three side faces of the triangular pyramid $(P-ABC)$ is at its maximum. What is the surface area of the sphere $(O)$?

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