
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 cube is inscribed in a hemisphere of radius \( R \) such that four of its vertices lie on the base of the hemisphere and the other four vertices are located on its spherical surface. Find the volume of the cube.

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