
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

On a chessboard of 8x8, 64 checkers are placed, numbered from 1 to 64. 64 students approach it one by one and flip only those checkers whose numbers are divisible by the order number of the current student. A "Queen" is a checker that has been flipped an odd number of times. How many "Queens" will be on the board after the last student steps away from it?

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