
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 vertex of a right angle is $O$, with legs $a$ and $b$. Points $A$ and $B$ move along the rays $a$ and $b$ such that $A O + O B$ is constant. On the circle with diameter $A B$, point $C$ is marked such that $O C$ is parallel to $A B$. What is the locus of points $C$?

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