
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 the line $l$: $x - y + 5 = 0$, circle $A$: $(x - 4)^2 + (y - 3)^2 = 4$, and point $B$($-2$, $-3$),
1. Find the maximum distance from a point on the circle to the line.
2. A light ray is emitted from point $B$ and reflects off line $l$, intersecting the circle. Find the range of possible slopes for the reflected light ray.

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