
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 solid has a triangular base with side lengths of $a$, $b$, and $c$. The upper face is parallel to the base and scaled by a factor of $2$. All other edges are of length $a$. Given that $a=6\sqrt{2}$, $b=6\sqrt{2}$, and $c=6\sqrt{2}$, calculate the volume of the solid.

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