
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 parabola $C: y^2=-4x$.
(Ⅰ) It is known that point $M$ is on parabola $C$ and its distance from the focus is equal to 5. Find the coordinates of point $M$.
(Ⅱ) Line $l$ passes through fixed point $P(1, 2)$ with slope $k$. What values of $k$ make the line $l$ have: only one common point; two common points; no common points with the parabola?

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