
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
A sphere with a surface area of $60\pi$ has four points $S$, $A$, $B$, $C$ on it. $\triangle ABC$ is an equilateral triangle, and the distance from the sphere's center $O$ to the plane $ABC$ is $\sqrt{3}$. If the plane $SAB$ is perpendicular to the plane $ABC$, find the maximum volume of the triangular pyramid $S-ABC$.

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