
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 circle C passes through points A(-2, 2) and B(2, 6), with its center C lying on the line 3x + y = 0.
(I) Find the equation of circle C.
(II) If a line l passes through point P(0, 5) and the length of the segment intercepted by circle C is $4\sqrt{3}$, find the equation of line l.

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