
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 lines \(OA\) and \(OB\) are perpendicular. Find the locus of the endpoints \(M\) of the line segments \(OM\) of length 1, such that any line parallel to \(OA\) or \(OB\) intersects the path no more than at one point.

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