
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 mutually perpendicular, and the sides of the base are $\sqrt{85}$, $\sqrt{58}$, and $\sqrt{45}$. The center of the sphere, which touches all the lateral faces, lies on the base of the pyramid. Find the radius of this sphere.

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