
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 base of a hexagonal prism is a regular hexagon, and the side edges are perpendicular to the base. It is known that all the vertices of the hexagonal prism lie on the same spherical surface, and the volume of the hexagonal prism is \(\frac{9}{8}\). The perimeter of the base is 3. Calculate the volume of the sphere.

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