
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 the ellipse $C: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$) with eccentricity $\frac{\sqrt{3}}{2}$, $F_1$ 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 $\triangle MF_1F_2$ 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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