
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
For finite sets  $A$  and  $B$ , call a function  $f: A \rightarrow B$  an \emph{antibijection} if there does not exist a set  $S \subseteq A \cap B$  such that  $S$  has at least two elements and, for all  $s \in S$ , there exists exactly one element  $s'$  of  $S$  such that  $f(s')=s$ . Let  $N$  be the number of antibijections from  $\{1,2,3, \ldots 2018 \}$  to  $\{1,2,3, \ldots 2019 \}$ . Suppose  $N$  is written as the product of a collection of (not necessarily distinct) prime numbers. Compute the sum of the members of this collection. (For example, if it were true that  $N=12=2\times 2\times 3$ , then the answer would be  $2+2+3=7$ .)

*Proposed by Ankit Bisain*

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