
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 $C: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 (a > b > 0)$ with eccentricity $e = \frac{\sqrt{3}}{2}$, $F_1$ and $F_2$ are the left and right foci of the ellipse, respectively. Point $M$ is a point on the ellipse that is not an endpoint of the major axis, and the perimeter of the triangle $\Delta MF_1F_2$ is $4+2\sqrt{3}$.
  
1. Find the equation of ellipse $C$.
2. Through the point $D(0,-2)$, draw the line $l$ that intersects the ellipse $C$ at points $A$ and $B$. Point $N$ satisfies the relation $\overrightarrow{ON} = \overrightarrow{OA} + \overrightarrow{OB}$ (where $O$ is the origin). Find the maximum value of the area of the quadrilateral $OANB$ and the equation of line $l$ when the area is at its maximum.

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