
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
Each printing letter has one digit engraved on it. To print twelve pages of a book, the required digits are as follows: $1,2,3,4,5,6,7,8,9,1,0,1,1,1,2$. Now, for a new book, 2011 printing letters are taken from the storeroom, and after typesetting, some letters are left over. How many pages does this book have at most? What is the minimum number of printing letters left over?

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