
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 $H$. The surface area is given by $A = 2\pi R^2 + 2\pi RH$. If the volume of the cylinder is given by $\pi R^2 H = \frac{V}{2}$, find the ratio $\frac{H}{R}$.

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