
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 $C: x^{2}+y^{2}=3$, and a line $l$ passing through point $A(-2,0)$.  
$(1)$ When the line $l$ is tangent to the circle $C$, find the slope of the line $l$.  
$(2)$ As the endpoint $B$ of line segment $AB$ moves on the circle $C$, find the trajectory equation of the midpoint $M$ of line segment $AB$.

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