
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 tetrahedron with four equilateral triangular faces has a sphere inscribed within it and a sphere circumscribed about it. Each face has a sphere externally tangent to it at its center and also tangent to the circumscribed sphere. If a point \( Q \) is chosen randomly inside the circumscribed sphere, find the probability that \( Q \) is inside the inscribed sphere or one of the four smaller spheres, assuming the radius of the circumscribed sphere is twice that of the original problem.

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