
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
In the Cartesian coordinate system, the trajectory equation of curve $E$ is $x^{2}+y^{2}=4$.  
$(1)$ If the line $l:y=kx-4$ intersects curve $E$ at two distinct points $C$ and $D$, and $\angle OCD=30^{\circ}$ (where $O$ is the origin), find the slope of the line $l$;  
$(2)$ If point $Q$ is a moving point on the line $l:x-y-4=0$, and two tangents $QM$ and $QN$ are drawn from $Q$ to curve $E$ with tangents at points $M$ and $N$, investigate whether the line $MN$ passes through a fixed point.

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