
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 the equation \[x^2 + y^2 = 2|x-y| + 2|x+y|\], determine the area of the bounded region that this equation describes.
A) \(8\pi\)
B) \(12\pi\)
C) \(16\pi\)
D) \(18\pi\)
E) \(20\pi\)

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