
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 room, there are 100 light bulbs arranged in a single row, numbered from left to right as 1, 2, 3, ..., 100. Each light bulb has a pull cord switch, and initially, all the light bulbs are turned off. Now, 100 students line up outside the door. The first student enters the room and pulls the switch of every light bulb numbered with a multiple of 1; then the second student enters and pulls the switch of every light bulb numbered with a multiple of 2; and so on; finally, the 100th student enters and pulls the switch of the light bulb numbered with a multiple of 100. After this process, which light bulbs are on?

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