
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, now numbered in order as 1, 2, …, 1997. Then, the strings of lamps numbered with multiples of 2 are pulled once; next, the strings of lamps numbered with multiples of 3 are pulled once; finally, the strings of lamps numbered with multiples of 5 are pulled once. Determine the number of lamps that remain lit after pulling the strings 3 times.

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