
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
Legend has it that the ancient Greek mathematician Archimedes' tombstone is engraved with a cylinder containing a sphere inscribed within it, where the diameter of the sphere is equal to the height of the cylinder. The "cylinder containing a sphere" was Archimedes' most proud discovery. In a model of "cylinder containing a sphere," if the volume of the sphere is $4\sqrt{3}\pi$, then the surface area of the cylinder in this model is ______.

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