What are the triggers for the reforms?

At the moment this:

Rome- Reach huge city and build an imperial palace in any of the Roman starting cities + Ankon, except for Rome itself.

Any idea approximately what turn this happens for a typical campaign with Rome as an AI. I will have to attack Rome to win the campaign and I would rather fight pre-Marian troops than legionnaires, Rome already seems way OP'ed than the other factions, their stats far exceed my best Spartan troops!