
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 an ellipse $E$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with an eccentricity of $\frac{\sqrt{3}}{2}$, the area of the quadrilateral formed by connecting the ellipse's four vertices is $16$.
(I) Find the equation of the ellipse $E$;
(II) A line $l$ passing through the vertex $P(0,b)$ of the ellipse $E$ intersects the ellipse at another point $M$ and intersects the $x$-axis at point $N$. If $|PN|$, $|PM|$, and $|MN|$ form a geometric sequence, find the slope of line $l$.

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