
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 the parabola C: y² = 4x, a line passes through the point (-1, 0) and is tangent to the parabola C at point P in the first quadrant.
(I) Find the coordinates of point P;
(II) If a line l passes through the point (2, 0) and intersects the parabola C at two points A and B, and a circle M with AB as the diameter passes through point P, find the equation of line l.

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