
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 and a cylinder have equal bases and equal heights. Their bases lie in the same plane and touch each other. Two spheres with radii equal to the radii of the bases of the cone and the cylinder touch each other, the lateral surfaces of the cone and the cylinder, as well as the plane containing the other base of the cylinder and the vertex of the cone. Find the angle at the vertex in the axial section of the cone.

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