
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
The solid shown has a square base of side length $s$, and a top edge parallel to the base and with length $2s$. All other edges connecting the base to the top have length $s$. On top of this solid, a triangular prism rests with its triangular base having sides $s$, $s$, and the top edge of the original solid, $2s$. If $s=8\sqrt{2}$, what is the total volume of the combined solid?

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