
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 line  $g$  and a point  $A$  outside  $g$  are given in a plane. A point  $P$  moves along  $g$ . 
Find the locus of the third vertices of equilateral triangles whose two vertices are  $A$  and  $P$ .

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