
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 its vertical edges aligned with the $z$-axis, and its base is a square with side length 6 centered at $(0,0,0)$. The vertices of the base are therefore:
\[
A = (3,3,0), \quad B = (3,-3,0), \quad C = (-3,-3,0), \quad D = (-3,3,0)
\]
The prism is cut by the plane $6x - 4y + 3z = 18$. Find the maximum area of the cross-section formed by this plane.

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