Painting - painting rough corners at wall/ceiling

At the area where the wall meets the ceiling, the corners are rough and it's a challenge cutting in. Little pits tend to pull in the paint and I'm getting a little (1/16" to 1/8") of wall paint on the ceiling here and then. When looking up at the corners, it doesn't look like a smooth job.

Should I caulk the corners before I paint to overcome this? Or, can I caulk now with white caulk. The ceilings are smooth (not-texture) and are ceiling white. Walls are brown.

Caulk could work. Cut the tip of a new tube as small a hole as possible. Run a tiny bead in the corner, smoothing it down as you go with a damp sponge. If its a small enough bead, it wont show up on the ceiling. Let it dry overnight before trying to paint on it.

I almost always end up caulking inside corners at the wall and ceiling joints where the taping is too sunken and it always makes it look cleaner. So no problem go for it.