
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 and a right circular cone are both inscribed in a sphere. The base radius of the cylinder is 4 units, and the sphere has a radius of 7 units. The cone shares the base with the cylinder and its vertex points toward the top of the cylinder. Calculate the total volume, in cubic units, of the space inside the sphere and outside the combined volume of the cylinder and cone. Let this volume be $X\pi$. Find $X$, as a common fraction.

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