
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
In the rectangular coordinate system xOy, it is known that the line $x + \sqrt{2}y - 2\sqrt{2} = 0$ is tangent to the ellipse C: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ ($a > b > 0$), and the right focus F($c$, $0$) of the ellipse C is symmetric about the line $y = \frac{c}{b}x$ with the point E on the ellipse C. Find the area of $\triangle$OEF.

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