
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 two perpendicular lines and a point, draw a circle around the point with an arbitrary radius so that it intersects both lines. At the intersection points, draw perpendiculars to the lines and find the intersections of these perpendiculars. What curve do the intersection points trace as the radius of the circle changes?

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