I think it is wrong. With strings of verbs, tense is governed by the first one conjugated, so the rest of the string should be free of tense inflections: "I wanted to took..."X "I did not taken... X" "I always enjoy eaten.... X"
So this sentence is in the present tense, as specified by I regret. The next verb needs to be a gerund in the present (taking), or a present continuous type of gerund (having taken). The past perfect infinitive "to have taken" doesn't match the present tense of the sentence as a whole.
PS. I'm describing the verbal structures in a way I find clear, but many books call them other names.