
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
The area of the region bounded by the graph of $x^2+y^2 = 4|x-y| + 4|x+y|$, express the area in the form $m+n\pi$ where $m$ and $n$ are integers, and find the value of $m + n$.

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