
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 the ellipse $C$: $x^{2}+ \frac{y^{2}}{4}=1$, the line $l$ passing through the point $M(0,1)$ intersects the ellipse $C$ at two points $A$, $B$.
(I) If $l$ intersects the $x$-axis at point $P$, and $P$ is the midpoint of $AM$, find the equation of the line $l$;
(II) Let point $N(0, \frac{1}{2})$, find the maximum value of $| \overrightarrow{NA}+ \overrightarrow{NB}|$.

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