
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 \( a\in \mathbb{R}\), the line \(l_1\): \(x+2y=a+2\) and the line \(l_2\): \(2x-y=2a-1\) intersect the circle \(E\): \((x-a)^2+(y-1)^2=4\) at points \(A\), \(C\) and \(B\), \(D\) respectively. Determine the area of the quadrilateral \(ABCD\).

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