
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 one thousand non-overlapping arcs on a circle, and two natural numbers are written on each of them. The sum of the numbers on each arc is divisible by the product of the numbers on the arc following it in the clockwise direction. What is the greatest possible value of the largest number written?

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