
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
Jiřka constructed two identical equilateral triangles as shown in the image. She wants to construct all circles that have their center at one of the vertices and pass through another vertex of either of the triangles.

Construct and calculate all circles that meet Jiřka's requirements.

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