
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 $\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$ ($a > b > 0$), the distance between the right vertex and the right focus is $\sqrt {3} - 1$, and the length of the minor axis is $2\sqrt {2}$.

(Ⅰ) Find the equation of the ellipse;  
(Ⅱ) A line passing through the left focus F intersects the ellipse at points A and B. If the area of $\triangle OAB$ (where O is the origin of the Cartesian coordinate system) is $\frac {3\sqrt {2}}{4}$, find the equation of line AB.

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