
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
In the complex plane, point $A$ corresponds to the complex number -2. Point $B$ moves on a circle centered at the origin with radius 1. Construct an equilateral triangle $ABC$ with $AB$ as one of its sides (with $A$, $B$, and $C$ arranged counterclockwise). Find the locus of the moving point $C$.

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