
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 $C$ with equation $(x-3)^2+(y-4)^2=4$, and line $l$ passing through point $A(1,0)$.

(I) If $l$ is tangent to circle $C$, find the equation of $l$.

(II) If $l$ intersects circle $C$ at points $P$ and $Q$, find the maximum area of triangle $CPQ$, and the equation of $l$ in this case (where point $C$ is the center of circle $C$).

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