
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
Given a regular tetrahedron $S-ABC$ with edge length $a$, there are four small spheres inside it, each with the same radius and each tangent to the others. Additionally, each sphere is tangent to the adjacent three faces of the tetrahedron. Determine the radius of the spheres.

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