
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 with its center at the origin and foci at $F_1(0, -2\sqrt{2})$ and $F_2(0, 2\sqrt{2})$, and its eccentricity $e= \frac{2\sqrt{2}}{3}$.  
(I) Find the equation of the ellipse;  
(II) A line $l$ (not parallel to the coordinate axes) intersects the ellipse at two distinct points A and B, and the x-coordinate of the midpoint of segment AB is $- \frac{1}{2}$. Find the range of values for the angle of inclination of line $l$.

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