
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 rectangular prism has its vertical edges parallel to the $z$-axis, and its cross-section is a rectangle with sides of lengths 8 and 12. Assume the bottom side lies in the $xy$-plane centered at the origin $(0,0,0)$. The prism is cut by the plane $3x + 5y - 2z = 30$. Find the maximum area of the cross-sectional cut by this plane.

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