
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
Three edges of a tetrahedron meeting at one vertex are mutually perpendicular with lengths 3, 4, and 4. Find the radii of the inscribed and circumscribed spheres of the tetrahedron.

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