
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 triangular prism ABC-A₁B₁C₁ has a right triangular base, and the length of its side edge is equal to the length of the hypotenuse of the base triangle. If the volume of its circumscribed sphere is $$\frac {32π}{3}$$, what is the maximum volume of the prism?

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