
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 cone has a base diameter equal to its slant height. Three identical spheres are placed inside the cone in such a way that they 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 that lies in the same plane as the centers of the spheres. Find the ratio of the radii of the base of the cone to the spheres.

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