
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 a circle $C: x^2 + y^2 - 4x + 2y + m = 0$ that intersects the y-axis at points A and B, and $\angle ACB = 90^\circ$ (C being the center of the circle), a line passing through point P(0, 2) with slope $k$ intersects circle C at points M and N.  
(Ⅰ) Find the value of the real number $m$;  
(Ⅱ) If $|MN| \geq 4$, find the range of $k$;  
(Ⅲ) If the vector $\overrightarrow{OM} + \overrightarrow{ON}$ is collinear with vector $\overrightarrow{OC}$ (O being the origin), find the value of $k$.

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