
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 $l: (m+2)x + (1-2m)y + 4m-2 = 0$ intersects the circle $C: x^{2} - 2x + y^{2} = 0$ at points $M$ and $N$. <br/>$(1)$ Find the coordinates of the fixed point that the line $l$ always passes through;<br/>$(2)$ Determine the range of values for the slope of the line $l$;<br/>$(3)$ If $O$ is the origin, and the slopes of lines $OM$ and $ON$ are $k_{1}$ and $k_{2}$ respectively, is $k_{1}+k_{2}$ a constant value? If yes, find the constant value; if not, explain the reason.

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