I think that means don’t play the first thing that pops into your head. Theoretically you would never select a move if you were always looking for a better one. Think long, think wrong…once you decide on the move you think best, play it and don’t second guess yourself.
Here’s an interesting observation I made in the now out of print Thought and Choice in Chess by DeGroot: When average (say 1600-1800) players were asked to analyze a position they looked at a lot more moves than GM’s. This is not surprising because GM’s quickly cut straight to the heart of the matter. But here’s the weird thing: in many positions the average players, often within the first 2-4 moves, looked at move the GM’s also looked at; even though the GM’s may have rejected the move, they still looked at it! The average players often talked themselves out of playing the move in their search for something better. You can gain a lot of rating points playing GM rejects.
Trust your instincts. Look at 3 or 4 moves and if in the process of evaluating them you aren’t lead to look at anything else, play the one that looks the most threatening even if it’s only in a general sort of way. Why not give it a try?
Regarding the solutions, in the first position only ...Re1 is correct, in the second position only Bc4 is correct (but no credit if you missed the cross-pin ...Ba6).