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

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