
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 triangular bases, given the sum of the areas of three mutually adjacent faces (two lateral faces and one base) is 40, and the angle between the sides of the base is $\frac{\pi}{3}$, find the maximum volume of the prism.

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