
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 rectangular solid has a square base, and the sum of the lengths of its edges is 24. When the volume of this solid is maximized, find the volume of its circumscribed sphere.

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