
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 has a square cross-section with each side measuring 12 units and vertical edges parallel to the $z$-axis. The vertices of the base square at the origin level are assumed to be at coordinates \((6, 6, 0)\), \((-6, 6, 0)\), \((-6, -6, 0)\), and \((6, -6, 0)\). The prism is intersected by the plane \(5x - 8y + 3z = 30\). Determine the maximum area of the cross-section created by this plane.

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