
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 $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with an eccentricity of $\frac{\sqrt{2}}{2}$ and a minor axis length of $2$.

1. Find the equation of the ellipse.
2. If line $l$: $y=x+\sqrt{2}$ intersects the ellipse at points $A$ and $B$, and $O$ is the origin, find the area of $\triangle AOB$.

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