
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 square-based right prism has base edges of $6 \text{ cm}$, and its side edges (segments $AA'$, $BB'$, $CC'$, and $DD'$) are $12 \text{ cm}$ long. Pyramids with vertices $(A A'B' D')$, $B B' A'C'C)$, $(C C' B' D')$, and $(D D' A' C')$ are cut from the prism. What is the volume of the remaining solid?

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