previous day/the day before

Yup.

Ms Tan, some idiots tried to make rules for reported speech with little regard to language and even less regard to reality.

Reported speech, like all other speech, uses the words that describe what the situation needs.

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Paul: [mumbles] I went to church yesterday.

Mary [to Tom] Paul's such a mumbler. What did he say?

Tom: He said that he went to church yesterday.

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Paul said that he had gone to church the previous day/the day before.

Without a context, 'the previous day/the day before' make no sense.

This is similar to those empty grammatical exercises that Japanese students have to do. They learn little from them because word choice is highly dependent upon the situation.