
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
A point $P$ on a sphere is chosen, and three chords $PA, PB, PC$ of the sphere, mutually perpendicular at $P$, are drawn. Given that $PA=PB=2\sqrt{2}$ and $PC=3$, find the radius of the sphere.

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