
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
Arrange 2002 students numbered from 1 to 2002 in a row from left to right. Counting from left to right from 1 to 11, the student who is counted as 11 remains in place, while the others leave the row. Then, the remaining students count from left to right from 1 to 11 again, and the student who is counted as 11 remains, while the others leave the row. Finally, the remaining students count from left to right from 1 to 11, and the student who is counted as 11 remains, while the others leave the row. How many students remain in the end? What are their numbers?

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