
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 three flies of negligible size that start at the same position on a circular track with circumference 1000 meters. They fly clockwise at speeds of 2, 6, and  $k$  meters per second, respectively, where  $k$  is some positive integer with  $7\le k \le 2013$ . Suppose that at some point in time, all three flies meet at a location different from their starting point. How many possible values of  $k$  are there?

*Ray Li*

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