
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 sphere with center $O$, there are four points on the surface of the sphere: $S$, $A$, $B$, and $C$, where points $O$, $A$, $B$, and $C$ are coplanar, and $\triangle ABC$ is an equilateral triangle with side length $2$. The plane $SAB$ is perpendicular to the plane $ABC$. Find the maximum volume of the tetrahedron $S-ABC$.

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