Check out these pics of Anna looking at houses in Venice, CA with serious boyfriend Michael Barrett. They checked out 2 homes ... super modern cribs, though not directly on the ocean.

TMZ broke the story ... Chris Pratt filed for divorce Friday and Anna filed her response at the exact same time. It's unclear who's living in the family home, but we're guessing it will be sold as part of the property settlement.

Unclear if Michael's moving in with Anna or whether he's just tagging along.