
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 circular cone $\Omega$ has a base radius of 2, and its lateral surface, when unfolded, is a sector with a central angle of 180°. A right square prism $ABCD-A'B'C'D'$ has its upper base vertices $A', B', C', D'$ on the lateral surface of the cone, and its lower base is on the base of the cone. Find the maximum volume of this right square prism.

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