
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
There are 100 light bulbs numbered 1, 2, 3, ... 100, each controlled by a switch. Initially, all of them are turned off. Now, 100 students enter the room one by one. When the first student enters, they toggle the switches of bulbs that are multiples of 1. Then, the second student enters and toggles the switches of bulbs that are multiples of 2. When the $n$-th student (where $n \leq 100$) enters, they toggle the switches of bulbs that are multiples of $n$. This process continues until the last student has entered and toggled the switch of the bulb that can be divided by 100. After this process, which bulbs are still on?

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