
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
A line passing through the origin intersects the ellipse $C: \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1\ (a > b > 0)$ at points A and B. Point P is another point on ellipse C that is different from A and B. The slopes of lines PA and PB both exist, and the product of the slopes of PA and PB is $-\frac{1}{4}$.
(1) Find the eccentricity of ellipse C;
(2) Let F<sub>1</sub> and F<sub>2</sub> be the left and right foci of ellipse C, respectively. A line l with slope k passes through the right focus F<sub>2</sub> and intersects the ellipse at points M and N. If point F<sub>1</sub> is inside the circle with diameter |MN|, find the range of values for k.

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