
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
Inside a regular tetrahedron with edge length \( a \), four identical spheres are placed such that each sphere touches the other three spheres and three faces of the tetrahedron. Find the radii of these spheres.

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