
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
Consider a solid with a hexagonal base where each side has length $s$. The upper face is also a hexagon, but scaled by a factor of 1.5 relative to the base and rotated about the vertical axis bisecting the base by 30 degrees. All vertical edges connecting corresponding vertices of the base and upper face have length $h$. If $s=4$ and $h=9$, find the volume of the solid.

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