
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 pyramid \(S-ABC\) with height \(SO = 3\) and a base whose side length is 6, a perpendicular is drawn from point A to its opposite face \(SBC\) with the foot of the perpendicular being \(O'\). On the line segment \(AO'\), a point \(P\) is selected such that \(\frac{AP}{PO'} = 8\). Find the area of the cross-section through point \(P\) and parallel to the base.

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