
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 solid with a right cylindrical middle part and two conical ends, each having the same radius $r$ as the cylinder. The fixed volume $V = 2k\pi r^2 h$ for some constant $k > 0.5$, and the height of each cone is equal to the radius $r$. Find the ratio $\frac{h}{r}$ to minimize the total surface area.

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