
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, with one of them equal to \(a\) and also equal to the sum of the other two. Find the radius of the sphere that touches the base of the pyramid and its lateral faces' extensions.

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