pursue , ***
follow up on
act on *

We will certainly follow up on that line of research.

He followed up for a second one on 27 April.

Head spent the next few years following up on his findings.

He never followed up on the people in his cases.

We spent another two days following up on everything you told us, but again, nothing.

But it's my job to follow up on all these things.

But the police never followed up on this piece of evidence.

You have to follow up on things that aren't done well.

But he had no idea how to follow up on that thought.

How are we going to follow up on this report?