
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 1997 lit lamps, each controlled by a pull string switch. They are sequentially numbered 1, 2, 3, …, 1997. First, pull the strings of lamps numbered with multiples of 2, then those with multiples of 3, and finally those with multiples of 5. How many lamps will remain lit after these actions?

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