
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 circular cone with a 90-degree vertex angle is placed on a table, pointing up. The diameter of the base of the cone is 24 inches. A sphere is placed inside the cone such that it is tangent to the sides of the cone and also rests on the table. Determine the volume of the sphere in cubic inches, expressing your answer in terms of \(\pi\).

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