
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
A fixed point  $A$  inside a circle is given. Consider all chords  $XY$  of the circle such that  $\angle XAY$  is a right angle, and for all such chords construct the point  $M$  symmetric to  $A$  with respect to  $XY$  . Find the locus of points  $M$ .

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