
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 rectangular prism has a square base of side length 8 and vertical edges parallel to the $z$-axis. The prism's height varies such that at vertices it rises to heights of 3, 2, 4, and 1 units, respectively. The prism is intersected by the plane given by the equation $3x - 5y + 3z = 24.$ Determine the maximal area of the resulting cross-section.

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