
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
Vasya drew several circles in the plane and drew all possible common tangents to each pair of these circles. It turned out that the drawn lines contain all the sides of a certain regular 2011-gon. What is the minimum number of circles Vasya could have drawn?

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