
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 that point $M$ is a moving point on the circle with center $E$ and equation $(x+ \sqrt {3})^{2}+y^{2}=16$, and point $F(\sqrt {3},0)$, with $O$ being the origin. The perpendicular bisector of segment $MF$ intersects $EM$ at point $P$.
$(1)$ Find the equation of the trajectory $H$ of point $P$;
$(2)$ A line $l$ passing through the origin $O$ intersects the trajectory $H$ at points $A$ and $B$. Point $C$ is on the trajectory $H$, and $|AC|=|CB|$. Point $D$ satisfies $\overrightarrow{CD}= \overrightarrow{CA}+ \overrightarrow{CB}$. Determine the range of the area of quadrilateral $ACBD$.

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