
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
In the Cartesian coordinate plane xOy, a circle C passes through the three intersection points of the parabola y=x^2-x-6 and the coordinate axes.
(1) Find the equation of circle C;
(2) A line l passing through the point P(-2, 5) intersects circle C at points A and B. If the tangents to circle C at points A and B are perpendicular to each other, find the equation of line l.

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