
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
We move the regular triangle \(ABC\) with unit side length in the domain of the \(120^\circ\) angle \(XOY\) in such a way that vertex \(A\) lies on the \(OX\) ray, vertex \(B\) lies on the \(OY\) ray, and the line \(AB\) separates point \(C\) from point \(O\). Determine the locus of vertex \(C\).

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