
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 250 colored light bulbs hanging in the activity room, numbered from $1$ to $250$. Their on-off rule is as follows: In the 1st second, all the light bulbs turn on; In the 2nd second, all the bulbs with numbers that are multiples of $2$ switch from on to off; In the 3rd second, all the bulbs with numbers that are multiples of $3$ change their current state (i.e., if they are on, they turn off, and if they are off, they turn on). In the $n$th second, all the bulbs with numbers that are multiples of $n$ change their current state. After 250 seconds, how many light bulbs are still on?

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