
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 number  $n$  is *interesting* if 2018 divides  $d(n)$  (the number of positive divisors of  $n$ ). Determine all positive integers  $k$  such that there exists an infinite arithmetic progression with common difference  $k$  whose terms are all interesting.

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