
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 2007 colored lights numbered 1, 2, 3, 4, …, 2007, all of which are turned on. If the first time you press the switch for all lights numbered with multiples of 2, the second time for lights numbered with multiples of 3, and the third time for lights numbered with multiples of 5, determine the number of lights that remain on.

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