
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 ${{(x+\\sqrt{3})}^{2}}+{{y}^{2}}=16$, point $F\\left( \\sqrt{3},0\\right)$, and $O$ is the coordinate origin. The perpendicular bisector of segment $MF$ intersects $EM$ at point $P$.

(1) Find the equation of the trajectory $H$ of moving point $P$;

(2) A line $l$ is drawn through the origin $O$ intersecting trajectory $H$ at points $A$ and $B$. Point $C$ is on trajectory $H$ such that $|AC|=|CB|$. Point $D$ satisfies $\\overrightarrow{CD}=\\overrightarrow{CA}+\\overrightarrow{CB}$. Find the range of values for the area of quadrilateral $ACBD$.

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