
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} = 9\\) at points \\(A\\), \\(C\\) and \\(B\\), \\(D\\) respectively. Then, the area of the quadrilateral \\(ABCD\\) is \_\_\_\_\_\_\_\_.

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