
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
Consider the points in the Cartesian coordinate system for which there exists a rectangle such that the first coordinate of the point is the perimeter of the rectangle, and the second coordinate is the area of the same rectangle. Characterize the region determined by these points.

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