
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 cone with a fixed volume $V,$ and the total surface area (including the base) needs to be maximized. Find the ratio of height $H$ to the radius $R$ of the base for which this occurs.

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