
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 that point $P$ is on circle $C$: $({x}^{2}+{y}^{2}=4)$, and $Q$ is the projection of $P$ on the $x$-axis, and point $N$ satisfies $\overrightarrow{PN}=\overrightarrow{NQ}$, determine the trajectory of point $N$ as curve $E$.
(I) Find the equation of curve $E$;
(II) If $A,B$ are two points on curve $E$, and $|AB|=2$, $O$ is the coordinate origin, find the maximum area of $\Delta AOB$.

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