
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 $F_1$ and $F_2$ are the left and right foci of the ellipse $C: \frac{x^2}{4} + y^2 = 1$.
(1) If $P$ is a point on the ellipse in the first quadrant, and $\overrightarrow{PF_1} \cdot \overrightarrow{PF_2} = -\frac{5}{4}$, find the coordinates of the point $P$;
(2) Let a line $l$ passing through a fixed point $M(0,2)$ intersect the ellipse at two distinct points $A$ and $B$, and let $\angle AOB$ be an acute angle (where $O$ is the origin). Determine the range of values for the slope $k$ of line $l$.

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