
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 regular triangular prism \( S-ABC \) with height \( S O = 3 \) and base side length of 6, a perpendicular is drawn from point \( A \) to the opposite face \( SBC \), with the foot of the perpendicular denoted as \( O' \). A point \( P \) is chosen on \( AO' \) such that \( \frac{AP}{PQ} = 8 \). Find the area of the cross-section passing through point \( P \) and parallel to the base.

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