
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 point $P(-2,-3)$ and circle $C$: $(x-4)^{2}+(y-2)^{2}=9$, draw two tangents from point $P$ to circle $C$, with the points of tangency being $A$ and $B$. Then, the equation of the circle passing through points $P$, $A$, and $B$ is __________.

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