
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 hexagonal prism has a regular hexagonal base, and its lateral edges are perpendicular to the base. It is known that all the vertices of the hexagonal prism are on the same spherical surface, and the volume of the hexagonal prism is $\frac{9}{8}$, with a base perimeter of 3. The volume of this sphere is ______.

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