
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 $C\_1$: $\frac{y^{2}}{16} + \frac{x^{2}}{4} = 1$, and another ellipse $C\_2$ with $C\_1$'s minor axis as its major axis, and having the same eccentricity as $C\_1$.
(I) Find the equation of the ellipse $C\_2$;
(II) If the ellipse $C\_2$ intersects the positive semi-axis of $x$ at point $A$, the line $l$ passing through point $B(1, 0)$ intersects the ellipse $C\_2$ at points $E$ and $F$, and lines $AE$ and $AF$ intersect lines $x=3$ at points $M$ and $N$ respectively. Find the range of values for $\overrightarrow{EM} \cdot \overrightarrow{FN}$.

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