
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 $C$: $(x-3)^{2}+(y-4)^{2}=4$.
- (I) If line $l$ passes through point $A(2,3)$ and the chord intercepted by circle $C$ has a length of $2\sqrt{3}$, find the equation of line $l$;
- (II) If line $l$ passes through point $B(1,0)$ and intersects circle $C$ at points $P$ and $Q$, find the maximum area of $\triangle CPQ$ and the equation of line $l$ at this condition.

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