
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 lights numbered from $1$ to $100$, each corresponding to a switch numbered from $1$ to $100$. The lights can be in either the "on" or "off" state, and each press of a switch changes the state of the corresponding light. All lights start in the "off" state. There are 100 people, where the first person presses all switches that are multiples of $1$ once, the second person presses all switches that are multiples of $2$ once, the third person presses all switches that are multiples of $3$ once, and so on, until the 100th person presses all switches that are multiples of $100$ once. How many lights are in the "on" state in the end?

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