
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
A right prism has vertical edges aligned with the $z$-axis, and its base is a square with a side length of 8. The vertices of the square base are at height $z=0$.

The prism is cut by the plane $3x - 5y + 2z = 20$. Calculate the maximum area of the cross-sectional cut formed by the plane.

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