here's the best algorithm for making decisions about pronouns:
0/
what thing/person/animal/whatever SHOULD the pronoun stand for?
(step zero, because it shouldn't be a "step" at this point; from reading the original sentence, you should already understand ALL aspects of intended meaning)
1/
is there a noun for that thing/person/animal/whatever?
..... if not, the pronoun is wrong (unless it's one of the VERY FEW exceptions--
link here).
..... if so, go to step 2.
2/
do the pronoun and noun match (singular/singular or plural/plural)?
if the answers to both #1 and #2 are yes, the pronoun is fine.
if the book contains such unnecessary complexity, i'll go ahead and submit it for removal. the point here--as for EVERY major topic in SC--is to keep things simple.