
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 $M: x^2 + y^2 = r^2$ ($r > 0$) is tangent to the line $l_1: x - \sqrt{3}y + 4 = 0$, and let point $A$ be a moving point on the circle, $AB \perp x$-axis at $B$, and the moving point $N$ satisfies $\overrightarrow{AB} = 2\overrightarrow{NB}$. Let the trajectory of the moving point $N$ be curve $C$.
(1) Find the equation of curve $C$;
(2) Line $l$ is perpendicular to line $l_1$ and intersects curve $C$ at points $P$ and $Q$. Find the maximum value of the area of $\triangle OPQ$.

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