
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 spheres of the same radius touch each other in pairs and a certain plane. The base of a cone is located in this plane. All three spheres touch the lateral surface of the cone externally. Find the vertex angle of the axial section of the cone if the height of the cone is equal to the diameter of the sphere.

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