
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
If the volume of a cone is equal to the volume of a sphere, and the radius of the base of the cone is equal to the diameter of the sphere, then the ratio of the lateral 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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