
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 $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (where $a > b > 0$) with an eccentricity $e = \frac{\sqrt{3}}{2}$, the area of the rhombus formed by connecting the four vertices of the ellipse is 4.

(Ⅰ) Determine the equation of the ellipse;

(Ⅱ) Let line $l$ intersect the ellipse at two distinct points $A$ and $B$, where point $A$ has coordinates $(-a, 0)$.

(i) If $|AB| = \frac{4\sqrt{2}}{5}$, find the slope angle of line $l$;

(ii) If point $Q(0, y_0)$ is on the perpendicular bisector of segment $AB$, and $\overrightarrow{QA} \cdot \overrightarrow{QB} = 4$, find the value of $y_0$.

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