[Cervantes]

Hi,
I'm a little confused about the following:

I know that this sentence is grammatically correct:

Karen enters the house, walks to the family room, sits, and starts watching TV.

However, is the following correct?

Karen enters the house, walks to the family room.

Or I must write.

Karen enters the house and walks to the family room.

What I try to find out is if I can drop the conjunction "and" and use a comma instead when the subject is the same for two action verbs.

Any light on this will be highly appreciated.

Thanks