
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 cylinder is inscribed in a sphere of radius $R$. When the lateral surface area of the cylinder is maximum, find the difference between the surface area of the sphere and that of the cylinder's lateral surface area.

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