
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 sphere with a radius of 1 unit can be inscribed in a tetrahedron. The planes parallel to the faces of the tetrahedron and tangent to the sphere cut off small tetrahedrons from the original tetrahedron. What is the sum of the radii of the spheres inscribed in these smaller tetrahedrons?

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