When to Anneal for Maximum Accuracy?

I was able to extend the life of thicker wsm brass before the necks split by annealing, nothing fancy though just a propane bottle and a cordless drill.
 
I am contemplating purchasing a annealing machine for the usual reason of extending brass life...but more importantly to improve accuracy by normalizing neck tension. Some competition shooters are annealing their brass every time they reload for maximum accuracy. My question is when, in the brass preparation process, is it more beneficial to anneal the brass...prior to FL or neck sizing (and possibly neck turning) or after? Does it make any difference in accuracy when you anneal the brass?

Anneal AFTER neck turning. The turning causes the neck brass to work harden. I lost a bunch of hard to find cases when I turned them, loaded them, and stored them in the winter, for an upcoming shoot... and 30% had "T" splits when I took them out of the boxes in late spring.
 
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