
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 creates a 4026-digit number from these cards. In one move, Petya can swap any two cards and pay Vasya 1 ruble. The process ends when Petya forms a number that is 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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