
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 2013 colored lights numbered 1, 2, 3, 4, …, 2013, all turned on, each controlled by a switch. If the first time you press the switch of all lights numbered with multiples of 2, the second time you press the switch of lights numbered with multiples of 3, and the third time you press the switch of lights numbered with multiples of 5, then the number of lights that remain on is     .

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