
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 center of a circle is the point with Cartesian coordinates \((a, b)\). It is known that the origin lies within the circle.

Let \(S^+\) denote the total area of the parts of the circle consisting of points whose coordinates both have the same sign, and let \(S^-\) denote the area of the parts consisting of points with coordinates of different signs. Find the value of \(S^+ - S^-\).

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