
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 $x^{2} +y^{2} =r^{2} (r > 0)$ and a line $l_{1}$: $x - \sqrt{3}y +4=0$ are tangent, let point $A$ be a moving point on the circle, $AB$ is perpendicular to the $x$-axis at $B$, and moving point $N$ satisfies $\overrightarrow{AB}=2\overrightarrow{NB}$, the trajectory of moving point $N$ is curve $C$.

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

(II) Line $l$ is perpendicular to line $l_{1}$ and intersects curve $C$ at points $P$ and $Q$, find the maximum area of $\triangle OPQ$.

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