
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
There are 2013 cards with the digit 1 and 2013 cards with the digit 2. Vasya arranges these cards to form a 4026-digit number. On each move, Petya can swap any two cards and pay Vasya 1 ruble. The process ends when Petya forms a number divisible by 11. What is the maximum amount of money Vasya can earn if Petya aims to pay as little as possible?

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