
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
Three identical spheres are placed inside a cone, where the diameter of the base of the cone is equal to the slant height. The spheres touch each other externally. Two of the spheres touch the lateral surface and the base of the cone. The third sphere touches the lateral surface of the cone at a point lying in the same plane with the centers of the spheres. Find the ratio of the radii of the base of the cone and the spheres.

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