
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
\[\sqrt{x-y} = \frac{2}{5}, \quad \sqrt{x+y} = 2\]

The solution \((x, y) = \left( \frac{52}{25}, \frac{48}{25} \right)\).

The points corresponding to the solutions are the vertices of a rectangle. The area of the rectangle is \(\frac{8}{25}\).

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