
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 with center P passes through point F(1, 0) and is tangent to the line x = -1.
(I) Find the equation of the trajectory C of point P;
(II) If A, B, C, and D are four points on the curve C such that AB is perpendicular to CD, they intersect at point F, and the angle of inclination of line AB is acute. If the area of the quadrilateral ACBD is 36, find the equation of line AB.

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