
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
There are spheres with radii 2, 2, and 5 lying on a table and touching each other externally. The apex of a cone is located in the middle between the points of contact of the identical spheres with the table, and the cone touches all the spheres externally. Find the angle at the apex of the cone. (The angle at the apex of the cone is defined as the angle between its generatrices in the axial section.)

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