
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
A line passing through the origin with a positive slope intersects the ellipse \(\frac{x^{2}}{4} + y^{2} = 1\) at points \(E\) and \(F\). Given points \(A(2,0)\) and \(B(0,1)\), find the maximum area of the quadrilateral \(AEBF\).

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