
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
In Problem 4, the angle at the vertex in the axial section of the cone is $60^{\circ}$. Outside this cone, there are 11 spheres with a radius of 3, each of which touches two neighboring spheres, the lateral surface of the cone, and the plane of its base. Find the radius of the base of the cone.

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