
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 with a radius of \(\sqrt{24}\) are placed in a cone, touching each other externally. Two spheres touch the lateral surface and the base of the cone. The third sphere touches the lateral surface of the cone at a point that lies in the same plane as the centers of the spheres. Find the radius of the base of the cone, given that it is equal to the height of the cone.

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