
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 a circle C with equation $(x-1)^2 + y^2 = 16$, there is a point P(2, 2) inside it. Let line l pass through point P and intersect circle C at points A and B.
(1) When line l passes through the center of circle C, find the equation of line l;
(2) When chord AB is bisected by point P, write the equation of line l.

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