
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
Joe has exactly enough paint to paint the surface of a cube whose side length is 3. It turns out that this is also exactly enough paint to paint the surface area (including both circular faces and the curved surface) of a cylinder. If the height of the cylinder equals its diameter and the volume of this cylinder is $\frac{J \sqrt{3}}{\sqrt{\pi}}$, what is $J$?

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