
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 cylindrical hole of 6 cm in length is drilled through a sphere, with the axis of the cylinder passing through the center of the sphere. What is the remaining volume? (Note: The volume of a spherical cap is $\pi h^{2}(R-h / 3)$, where $R$ is the radius of the sphere and $h$ is the height of the cap.)

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