
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
A teacher made 50 cards for their class of 50 students, each card labeled with a number from 1 to 50. Each card has one red side and one blue side, with the same number printed on both sides. The teacher initially places all 50 cards blue side up on the table and tells the students: "Each of you will take turns flipping cards following this rule: If any card has a number that is a multiple of your own student number, flip it. If it's blue, flip it to red; if it's red, flip it to blue."

How many cards are having their red side up after all students have followed the flipping rule?

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