Assassin do breed, but only if there is a pair, and only one egg is laid at a time.
They cannot reproduce on own like some snails can.
Here is a pic of an assassin snail egg from my tank, and yes, its a SQUARE egg! Well, a square transparent pouch with a yellow egg inside.
Once eggs are hatched, the tiny assassins will quickly hide, usually in the substrate and you won't really see them until they grow a little larger.
But fascinating to see these eggs and TINY assassins, although assassin will only really reproduce when they are happy in an established tank, it took a few months before i saw the first eggs in my tank.
Very best of luck with this, and DO write a journal about this if you want to, I for one, would truly be fascinated to see how you get on
BTW - they do 'smooch' for days at a time!!