
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 a cylinder of fixed volume \( V \), the total surface area (including the two circular ends) is minimized for a radius \( r \) and height \( h \). Given that the volume is expressed as \( V = \pi r^2 h \), find the ratio \( \frac{h}{r} \) when the total surface area \( A = \pi r^2 + 4 \pi rh \) is minimized.

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