
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 triangular prism has its vertical edges parallel to the $z$-axis. Its cross-section is an equilateral triangle with a side length of 8. Each vertical edge has a different height: the first edge is 2 units high, the second is 4 units, and the third is 3 units. The prism is cut by the plane $5x - 3y + 2z = 30$. Find the maximal area of the cross-section.

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