
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 \( PO \) of the regular quadrilateral pyramid \( PABC D \) is 4, and the side of the base \( ABCD \) is 6. Points \( M \) and \( K \) are the midpoints of segments \( BC \) and \( CD \). Find the radius of the sphere inscribed in the pyramid \( PMKC \).

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