
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
Determine the smallest natural number  $n =>2$  with the property:
 For every positive integers  $a_1, a_2,.  .  .  , a_n$   the product of all  differences  $a_j-a_i$ , 
   $1 <=i <j <=n$ , is divisible by 2001.

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