
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 prism has triangular bases, and the sum of the areas of three mutually orthogonal faces (two distinct lateral faces and the base) is 30. The ratio of the longer side to the shorter side of the base triangle is fixed at 3:1. Determine the maximum possible volume of the prism.

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