In Puzzle 9, your opponent has shown you that they have a strong rack and can bingo with an open E (REINSERT and others) O (INTRORSE) G (RESTRING or STRINGER) and others. Because of this, you shouldn’t play a bingo such as fOREIGNER, but instead should make a play that does not give him a bingo. Without a bingo, your opponent is forced to fish and score very few points, with no guarantee that they will get a bingo next turn.
REI is a stronger play than REIGN. REI forces your opponent to fish an R, and you can respond by either scoring next turn or trading your stronger racks. REI makes it difficult for your opponent to play a bingo, and any bingo that your opponent does draw will allow you to counter-bingo, and possibly even get to play a triple-triple using your blank.
Note that there will be certain racks with which you may not want to bingo next turn, since you will often give your opponent a 3×3. For example, you may not want to play a bingo along column e that ends in G, as it allows your opponent to draw several 3x3s with the G in the 5th spot (STINGIER, INTEGERS, and STINGERS), which will occur about 25% of the time.