
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
During careless transportation of printing paper rolls, cracks appear on their surface, resulting in paper waste that goes to scrap. Obviously, this waste is minimized when the total surface area of the roll, given its volume, is minimized. It is necessary to investigate at what ratio between the diameter and the length (i.e., the generatrix) of the roll the paper waste will be minimal.

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