
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
In a sphere $O$ with a radius of $4$, there is an inscribed cylinder. When the lateral surface area of the cylinder is at its maximum, the difference between the surface area of the sphere and the lateral surface area of the cylinder is ______.

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