
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 height of a pyramid is 5, and the base is a triangle with sides 7, 8, and 9. A sphere touches the planes of all the lateral faces of the pyramid at points lying on the sides of the base. Find the radius of the sphere.

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