
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 $xOy$, points $M(-2 \sqrt {2}, 0)$ and $N(2 \sqrt {2}, 0)$ are given. If line $m$ is perpendicular to $MN$ at point $D$, and point $C$ is a moving point on line $m$. Let $H$ be the midpoint of segment $CD$, and $\overrightarrow{NH} \cdot \overrightarrow{MC} = 8$. The locus of point $H$ is curve $E$.  
$(1)$ Find the equation of curve $E$.  
$(2)$ Draw line $l$ passing through point $A(-4, 0)$ intersecting $E$ at point $P$ and the $y$-axis at point $Q$. Draw line $l'$ parallel to $l$ through $O$, and $l'$ intersects $E$ at point $R$. Determine whether $\dfrac {|AQ|\cdot |AP|}{|OR|^2}$ is a constant value. If it is, find the value; if not, explain the reason.

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