
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 side of the base of a regular quadrangular pyramid is equal to \(a\), and the lateral edge is equal to \(b\). Find the radius of the sphere that touches the sides of the base and the extensions of the lateral edges of the pyramid.

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