Jack, I think you made this analysis unnecessarily complex for yourself. Simply think of it this way. Present tense: have to go, eat, sleep, write Different forms of past tenses: had to go, eat, sleep, write have had to go, eat, sleep, write had had to go, eat, sleep, write In other words, go eat, sleep and write do not change forms.
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AnonymousSo what can use with did? Did she has or did she have?Did she have...?