Er, isn't that basically a noun + complement rather than "two verbs in series"? (And transforming it to apparent underlying meanings doesn't help: A need exists to react to new opportunities with speed; ?To react to new opportunities with speed is necessary; etc (?)).(The title of the section is 'Talking about closely linked actions: using two verbs together in phase'. I've omitted sections 3.183 - 3.185, and obviously all that follows 3.186)
verb forms 3.186 The first verb involved in a phase structure is the main verb of the structure. It is usually finite; that is, it inflects for tense and agrees in number with the subject of the clause.
I wanted him to come.
Lonnie wants to say 'sorry'.
More and more people are coming to appreciate the contribution which Muslims make to our society.
However, it can be a non-finite form.
There is a need to react to new opportunities with speed.
I guess examples of non-finite, dependent clauses, such as Not wishing to boast, he paused (adapting an example from chapter 8, by reversing its clauses) might be more what COBUILD was suggesting?