
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 larger cube with an edge twice the original length. Compute the ratio of the volume of the sphere to the volume of the cube, and additionally compare the ratio of their surface areas. Express your answers as common fractions in terms of $\pi$.

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