
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 regular tetrahedron has all its edges equal to $s$. A sphere is inscribed within it, and another sphere is circumscribed about it. For each of the four faces, there is a sphere that is tangent externally to the face at its center and to the circumscribed sphere. Additionally, there are two smaller spheres inside, each tangent to three of the tetrahedron's edges and to the inscribed sphere. A point $P$ is chosen at random inside the circumscribed sphere. Calculate the probability that $P$ lies inside one of the seven spheres.

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