
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 line $l$ passing through point $A(2, 2)$ and a circle $C: x^2 + y^2 - 6x + 8 = 0$.
(1) Find the general equation of line $l$ when it is tangent to the circle.
(2) If the line intersects the circle and the chord length is $\sqrt{2}$, find the general equation of line $l$.

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