
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 an $8 \times 8$ chessboard, 64 checkers numbered from 1 to 64 are placed. 64 students, one by one, approach the board and flip only those checkers whose numbers are divisible by the ordinal number of the current student. A "king" (or "crowned" checker) is a checker that has been flipped an odd number of times. How many "kings" will there be on the board after the last student steps away?

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