
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 the 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 two points $A$ and $B$. If the area of $\triangle OAB$ ($O$ is the origin of the coordinate system) is $\frac{3\sqrt{2}}{4}$, find the equation of the line $AB$.

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