
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
An ellipse with the equation $\frac{x^{2}}{5} + \frac{y^{2}}{4} = 1$ has its right focus at point $F$. A line with a slope of $2$ passing through $F$ intersects the ellipse at points $A$ and $B$. If $O$ represents the origin, find the area of triangle $OAB$.

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