
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 that the left and right foci of the ellipse $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ are $F_{1}$ and $F_{2}$, and point $A(2, \sqrt{2})$ is on the ellipse, with $AF_{2}$ perpendicular to the $x$-axis.
(1) Find the equation of the ellipse;
(2) Draw a line through $A$ intersecting the ellipse at another point $B$, and find the maximum area of $\triangle AOB$.

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