
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]


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In the cartesian coordinate plane $(xOy)$, two circles $C\_1$ and $C\_2$ are given, where $C\_1: (x+3)^2+(y-1)^2=4$ and $C\_2: (x-4)^2+(y-5)^2=1$.

(I) If a line $l$ passes through point $A(4,0)$ and the chord length that $C\_1$ intercepts on $l$ is $2\sqrt{3}$, find the equation of line $l$.

(II) If a bundle of light rays is emitted from the center of circle $C\_1$ and is reflected by line $x-y-3=0$, then the reflected line intersects circle $C\_2$. Find the range of the slope of the reflected line.

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