What is going on in phase$\_5$ and what should the input be so that explode$\_$bomb does not run:

The value in the memory at $\%$rsp $($our input$)$ is masked with and $$0$xf$,\%$eax, retaining only the last $4$ bits of the integer $($values from $0$ to $15).$ I think to avoid explode$\_$bomb, the masked input and the array values must add up in a specific way to reach some number $($maybe $15)$ with exactly $14$ steps.