
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
In a card flipping game during a math class, the teacher numbered 54 playing cards in the order of 1, 2, 3, …, 54 and placed them face down in a row. There were exactly 54 students in the class, who were also numbered in the order of 1, 2, 3, …, 54. The rules of the game were as follows: the student numbered 1 flipped over all the cards that were multiples of 1; the student numbered 2 flipped over all the cards that were multiples of 2; the student numbered 3 flipped over all the cards that were multiples of 3, and so on, until the last 54th student flipped over card number 54 to end the game. The question is: how many playing cards were face up at the end of the game? List their numbers and explain the reason.

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