
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 sphere with radius $r$ is inside a cone, whose axial section is an equilateral triangle with the sphere inscribed in it. The ratio of the total surface area of the cone to the surface area of the sphere is \_\_\_\_\_\_.

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