
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 moving line $l$ passing through the origin $O$ and intersecting the circle $C: (x+1)^2+y^2=4$ at points $A$ and $B$.

(Ⅰ) If $|AB|=\sqrt{15}$, find the equation of line $l$;  
(Ⅱ) Is there a fixed point $M(x_0, 0)$ on the x-axis, such that the sum of the slopes of lines $MA$ and $MB$ is always zero as $l$ varies? If it exists, find the value of $x_0$; if not, explain why.

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