
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 a circle $M:x^{2}+y^{2}=r^{2} (r > 0)$ and a line $l_{1}:x-\sqrt{3}y+6=0$ are tangent to each other, let point $A$ be a moving point on the circle, $AB\bot x$ axis at $B$, and the moving point $N$ satisfies $\overrightarrow{AB}=\sqrt{3}\overrightarrow{NB}$. Let the trajectory of the moving point $N$ be curve $C$.

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

$(2)$ If line $l$ is perpendicular to line $l_{1}$ and intersects curve $C$ at points $B$ and $D$, find the maximum value of the area of $\Delta OBD$.

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