
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
Given that $A$ and $B$ are two moving points on the circle $C: (x-3)^{2} + (y-1)^{2} = 9$, and $|AB| = 2\sqrt{5}$, if $P(0,-3)$, then calculate the maximum distance from point $P$ to the line $AB$.

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