
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 2012 students standing in a circle; they are numbered \(1, 2, \ldots, 2012\) clockwise. The counting starts from the first student (number 1) and proceeds around the circle clockwise. Alternate students will be eliminated from the circle as follows: The first student stays in the circle while the second student leaves the circle. The third student stays while the fourth student leaves, and so on. When the counting reaches number 2012, it goes back to number 1 and the elimination continues until the last student remains. What is the number of the last student?

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