
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
In the regular prism $S-ABC$, where $AB = 4$ and $\triangle ABC$ is an equilateral triangle. $A'$, $B'$, and $C'$ are the midpoints of $SA$, $SB$, and $SC$ respectively. Let $D$ be the midpoint of $A'B'$, and let the circumsphere of the tetrahedron $S-ABC'$ have center $O$. Given that $OC^2 - OD^2 = AB^2$, find the volume of $S-ABC$.

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