
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
In the rectangular coordinate system on a plane, a line segment $AB$ of length $3$ has its endpoints $A$ and $B$ sliding on the $x$ and $y$ axes, respectively. Point $M$ is on line segment $AB$, and $|AM|=2|MB|$.
(1) Find the equation of the trajectory curve $C$ of point $M$;
(2) A line $l$ passing through point $P(0,1)$ intersects curve $C$ at two distinct points $E$ and $F$. $N$ is a moving point on the curve other than points $E$ and $F$. Find the maximum area of triangle $NEF$.

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