
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 sphere is inscribed in a cube with edge length 12 inches. A smaller cube is then inscribed in this sphere. Calculate the volume of the smaller inscribed cube in cubic inches, expressing your answer in simplest radical form.

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