I have to admit that I quite often "forget" to empty my inbox. After a couple of days, it gets quite some work to empty the box. Thus, I sometimes do it in two steps:
Step 1: Decide whether the item is trash or actionable or should be filed (coming up with a file pile and an action pile).
Step 2: then I start to file the items in the file pile and to organise the actionable items into the system.
I think this is an example where you separate processing (step 1) and organising (step 2).