
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 equation of the parabola is $y^{2}=-4x$, and a line $l$ passes through the fixed point $P(2,-1)$ with a slope of $k$, find the value of $k$ when the line $l$ and the parabola:

$(1)$ have only one intersection point;

$(2)$ have two common points.

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