
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: $(x-1)^2+y^2=9$ with a point P(2, 2) inside it. A line $l$ passes through point P and intersects circle C at points A and B.  
(1) When $l$ passes through the center of the circle C, find the equation of line $l$;  
(2) When chord AB is bisected by point P, write the equation of line $l$;  
(3) When the slope of line $l$ is 45°, find the length of chord AB.

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