
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 O, foci on the x-axis, and eccentricity $\frac{\sqrt{3}}{2}$, which passes through the point $(\sqrt{2}, \frac{\sqrt{2}}{2})$.
(Ⅰ) Find the equation of the ellipse;
(Ⅱ) If a non-horizontal line l intersects the ellipse at points P and Q (not passing through the origin O), and the slopes of OP, PQ, and OQ form a geometric sequence, find the slope of the line l.

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