
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
Given points \(A\) and \(B\), determine the locus of points \(C\) in the plane for which the area of triangle \(ABC\) is less than half the area of any square constructed on either side of the triangle.

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