
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 $\frac{x^2}{4} + y^2 = 1$ with its left and right foci being $F_1$ and $F_2$ respectively,

(I) If $P$ is a moving point on the ellipse, find the maximum and minimum values of $\overrightarrow{PF_1} \cdot \overrightarrow{PF_2}$;

(II) Suppose a line $l$ passes through the fixed point $M(0, 2)$ and intersects the ellipse at two distinct points $A$ and $B$, and $\angle AOB$ is acute (where $O$ is the origin). Determine the range of slope $k$ of the line $l$.

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