
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 with four equilateral triangular faces has a sphere inscribed within it and another sphere circumscribed about it. Each of the four faces of the tetrahedron is tangent to a unique external sphere which is also tangent to the circumscribed sphere, but now these external spheres have radii larger than those in the original setup. Assume new radii are 50% larger than the radius of the inscribed sphere. A point $P$ is selected at random inside the circumscribed sphere. Compute the probability that $P$ lies inside one of these external spheres.

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