
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
The angle at the apex of the axial section of a cone is $60^{\circ}$. Inside the cone, there are three spheres with a radius of 1. Each sphere is tangent to the other two spheres, the base of the cone, and its lateral surface. Find the radius of the base of the cone.

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