
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 right circular cone S-ABC, all of whose vertices lie on the same spherical surface, the base ABC is an equilateral triangle and is on the same plane as the sphere's center O. If the maximum volume of this right circular cone is $16\sqrt{3}$, find the surface area of sphere O.

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