
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
Given the perimeter of a rectangle is 30 cm, and the rectangle rotates around one of its edges to form a cylinder. What are the length and width of the rectangle when the lateral surface area of the formed cylinder is maximized? What is the maximum value of the lateral surface area?

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