
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
What is the maximum area of a rectangle whose vertex coordinates satisfy the equation \(|y - x| = (y + x + 1)(5 - x - y)\) and whose sides are parallel to the lines \(y = x\) and \(y = -x\)? Write the square of the value of the found area in the answer.

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