
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
Call a positive integer  $n$   $k$ *-pretty* if  $n$  has exactly  $k$  positive divisors and  $n$  is divisible by  $k$ . For example,  $18$  is  $6$ *-pretty*. Let  $S$  be the sum of positive integers less than  $2019$  that are  $20$ *-pretty*. Find  $\tfrac{S}{20}$ .

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