
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 points $A(-4,-3)$ and $B(2,9)$, circle $C$ has $AB$ as its diameter.
(1) Find the equation of circle $C$;
(2) Let point $P(0,2)$, then find the equation of line $l_{0}$ where the chord with $P$ as its midpoint lies.

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