
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 Cartesian coordinate plane $(xOy)$, point $M$ is located in the first quadrant of the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{12} = 1$, and points $A(2, 0)$ and $B(0, 2\sqrt{3})$ are the two vertices of the ellipse. Find the maximum area of the quadrilateral $OAMB$.

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