
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 on a 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 that Vasya could have drawn?

(N. Agakhanov)

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