
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 curve $M$ consists of the parabola $x^{2}=-y$ and the parabola $x^{2}=4y$, the line $l$: $y=kx-3$ ($k > 0$) intersects curve $M$ at $m$ ($m\in\mathbb{N}$) points.  
$(1)$ If $m\geqslant 3$, find the minimum value of $k$;  
$(2)$ If $m=4$, label the $4$ intersection points from top to bottom as $A$, $B$, $C$, $D$, and find the range of $\dfrac {|AB|}{|CD|}$.

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