
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 prism with a square base of side length 12 is oriented such that its vertical edges are parallel to the $z$-axis. The square base is centered at the origin $(0,0,0)$. The prism is cut by the plane $3x - 5y + 2z = 30$. Determine the maximum area of the cross-section formed by this plane cut.

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