If the -ing form of a verb is used as the main verb of the predicate, the auxiliary must contain a form of 1) be 2) do 3) have 4) will 5) none of these

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Its Be.
Here let me show you why.
I will BE doing, She will BE sleeping. Sounds correct.
I will do sleeping, she will do walking. Nope. Sounds wrong.
I will have sleeping : nopee.
I will sleeping no.
So the correct answer is BE