
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 O with a radius of $3 \sqrt{2}$, let S, A, B, and C be four points on the surface of the sphere, where $\angle ABC=90^{\circ}$ and $AB=BC=4 \sqrt{2}$. Find the maximum volume of the pyramid S-ABC.

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