
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
In a right prism with a rectangular base, the sum of the areas of two adjacent lateral faces and one base is 36. If the sides of the base are twice as long as the height of the prism, find the maximum volume of the prism.

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