
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 an ellipse $C:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1 (a > b > 0)$ with eccentricity $\dfrac{\sqrt{3}}{2}$, $F_1$ and $F_2$ are the left and right foci of the ellipse, respectively. $M$ is any point on the ellipse other than the endpoints of the major axis, and the perimeter of $\Delta MF_1F_2$ is $4+2\sqrt{3}$.

(1) Find the equation of ellipse $C$;

(2) A line $l$ passing through point $D(0,-2)$ intersects the ellipse $C$ at points $A$ and $B$. Point $N$ satisfies $\overrightarrow{ON}=\overrightarrow{OA}+\overrightarrow{OB}$ (where $O$ is the origin). Find the maximum area of quadrilateral $OANB$ and the equation of line $l$ at this time.

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