
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 circle C: $(x-3)^2+(y-4)^2=4$, and line $l$ passes through point $A(1,0)$.
(1) If $l$ is tangent to circle C, find the equation of $l$;
(2) If $l$ intersects circle C at points $P$ and $Q$, and $|PQ|=2\sqrt{2}$, find the equation of $l$ in this case.

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