
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 right circular cone with a height of 12 cm and a base radius of 5 cm has a sphere inscribed within it and a sphere circumscribed about it. For the circular base and three equally spaced points along the height of the cone, small spheres are tangent externally to the cone at these points and to the circumscribed sphere. A point $P$ is chosen at random inside the circumscribed sphere. The probability that $P$ lies inside one of the four small spheres is to be determined.

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