How do you reconcile anatman (denial of the individual soul) with samsara and nirvana?

Answer 1

I'd interpret Anatman as denial of the individual PERSONALITY, not the individual soul in all senses of the word. It has often been argued that what Buddha denied was whether the five skandhas lasted long enough to fit the definition of Atman that was current back then: an unchanging ever lasting essence that can be identified with one of the five skandhas. In the second sermon Buddha goes by them one by one. The body doesn't last. The emotions are fleeting. The mind changes. (I forget one) The sense of conciousness changes -so none of these last. None of these are constant.

That's where the text ends. This does not automatically mean that beyond consciousness isn't something else that does last - which would reincarnate untill purified enough to not cling to life any more - and then reach nirvana.