
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
A moving point $P$ is taken on the circle $x^{2}+y^{2}=3$. A vertical line $PD$ is drawn from $P$ to the $x$-axis, with $D$ as the foot of the perpendicular. If $\overrightarrow{PD}= \sqrt {3} \overrightarrow{MD}$, the locus of the moving point $M$ is a curve $C$.

1) Find the equation of $C$ and its eccentricity;

2) If a line $l$ intersects the curve $C$ at points $A$ and $B$, and the distance from the coordinate origin to the line $l$ is $\dfrac { \sqrt {3}}{2}$, find the maximum area of $\triangle AOB$.

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