Assassin snails hunt, kill, and eat other snails. Unfortunately, unless you get quite a large amount of assassin snails, they won't kill the invasive snails as quickly as the invasive snails breed. In addition to that, you always run the risk of the assassin snails breeding and over-running the tank.
You could make a couple of snail traps. Simply use a glass jar with a plastic lid. Drill 2 1/3 to 1/2 inch holes in the lid, put a few sinking pellets in the jar, fill with water and leave on your tank bottom overnight. Several snails will be inside each trap in the morning. Repeat as necessary.
The very best way to eradicate snails, however, is with either Yoyo or Clown loaches. Both are voracious eaters of snails. If your tank is on the smaller side, under 75 gallons, Yoyo loaches would be best, as they stay fairly small. If you have a larger tank, clown loaches work well. Both are fun fish to have, and easy to care for. Both species do best in small groups of 3 or more. Both will probably have your tank devoid of snails within a couple weeks.