Cast Persist by paying ({1} magic symbol) ({B} magic symbol) , returning Archaeomancer from your graveyard to the battlefield with a -1/-1 counter on it.
Archaeomancer enters the battlefield, triggering itself and Inalla.
Resolve the Archaeomancer trigger, returning Burnt Offering from your graveyard to your hand.
Resolve the Inalla trigger, causing you to pay ({1} magic symbol) to create a token copy of Archaeomancer with haste.
The token Archaeomancer enters the battlefield, returning Persist from your graveyard to your hand.
Repeat.
Once you have infinite Archaeomancer tokens, if Inalla is on the battlefield, you may activate Inalla's ability infinite times to cause infinite lifeloss for opponents.