
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
If the ratio   $$ \frac{17m+43n}{m-n} $$   is an integer where  $m$  and  $n$  positive integers, let's call  $(m,n)$  is a special pair. How many numbers can be selected from  $1,2,..., 2021$ , any two of which do not form a special pair?

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