
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
The lateral edges of a triangular pyramid are pairwise perpendicular, and the areas of the lateral faces are \( S \), \( P \), and \( Q \). Find the radius of the inscribed sphere. Also, find the radius of the sphere that touches the base and the extensions of the lateral faces of the pyramid.

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