
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
Suppose the transformation  $T$  acts on points in the plane like this:  $$ T(x, y) =  \left( \frac{x}{x^2 + y^2}, \frac{-y}{x^2 + y^2}\right). $$  Determine the area enclosed by the set of points of the form  $T(x, y)$ , where  $(x, y)$  is a point on the edge of a length- $2$  square centered at the origin with sides parallel to the axes.

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