
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
A thousand non-overlapping arcs are placed on a circle, and each arc has two natural numbers written on it. The sum of the numbers on each arc is divisible by the product of the numbers on the arc that follows it in a clockwise direction. What is the maximum possible value of the largest number written?

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