
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 circle $C$ passes through points $M(3,-3)$ and $N(-2,2)$, and the length of the line segment it intercepts on the $y$-axis is $4 \sqrt {3}$.
(I) Find the equation of circle $C$;
(II) If line $l$ is parallel to $MN$, and intersects with circle $C$ at points $A$ and $B$, and the circle passing through the origin with $AB$ as the diameter, find the equation of line $l$.

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