
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 right cylinder with a base radius of 4 units and a height of 10 units is inscribed in a sphere of radius 6 units. A right circular cone with the same base as the cylinder and a height of 10 units is also inscribed inside the cylinder. The total volume, in cubic units, of the space inside the sphere and outside both the cylinder and the cone is $W\pi$. Find $W$, expressed as a common fraction.

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