
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 region is enclosed by the graph of the equation \[x^2 + 4y^2 = 4|x-y| + 4|x+y|\]. Find the area \(A\) of this region, expressed in the form \(A = k + n\pi\), where \(k\) and \(n\) are integers.
A) \(6\)
B) \(8\)
C) \(10\)
D) \(12\)

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