
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
On two perpendicular axes \(OX\) and \(OY\), we choose two points, \(A\) and \(B\), such that \(OA + OB\) equals a constant \(k\). From point \(O\), we draw a line parallel to \(AB\), which intersects the circumcircle of triangle \(AOB\) at point \(M\). What is the locus of point \(M\)?

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