
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
A steam boiler consists of a cylinder with a hemisphere at each end. If we change the length and the width of the cylinder such that the total length of the boiler remains constant, what dimensions of the cylinder will maximize the volume of the boiler?

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