
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

Through $S$ and $V$ are denoted the surface area and volume of a regular $n$-sided pyramid.

a) For given values of $n$ and $S$, find the maximum value of $V$.

b) Find the side lengths of the base and the heights of all pyramids for which $n = 4$, $S = 144$, and $V = 64$.

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