
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 point P(6, 4) and circle C: $x^2+y^2-6x+4y+4=0$  
(1) When line $l$ passes through point P and is tangent to circle C, find the equation of line $l$;  
(2) Suppose a line passing through point P intersects circle C at points A and B, when $|AB|=3\sqrt{2}$, find the equation of line AB.

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