tall tree with smooth green leaves, many purple berry clusters

There is a very tall, 25-30 foot tree in my backyard. I am curious as to what it is. The leave have not turned at all given that it's December, and now there are large amounts of blueish/purple berries in clusters all over the tree. They are falling to the gound and I have cats that play in the yard so I'd like to identify the tree and berries.

I've included some photos. I was thinking maybe a Privet, but photos of those looked like bushes. This is a large tree with smooth bark.

 

Chinese Privet Ligustrum lucidum. A tree-size privet, and invasive in your area.

 

Thanks so much!!!!
Are the berries poisonous to animals? Cat's mainly.

 

Mildly poisonous to people (eating one might make you feel uncomfortable, but not in danger; ten would be nasty, 100 might be lethal), but fully edible for birds. Sorry, don't know about cats.