
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
A line $l$ passes through the point $P(-3,-4)$. Find the slope of $l$ when:
$(1)$ $l$ bisects the circle $(x-1)^{2}+(y+2)^{2}=4$?
$(2)$ $l$ is tangent to the circle $(x-1)^{2}+(y+2)^{2}=4$?
$(3)$ $l$ intersects the circle $(x-1)^{2}+(y+2)^{2}=4$ and the length of the chord is $2$?

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