en_tn_condensed/deu/13/14.md

examine the evidence, make search, and investigate it thoroughly

All of these phrases mean basically the same thing. Moses is emphasizing that they must carefully find out what truly happened at the city. (See: rc://en/ta/man/jit/figs-doublet)

that such an abominable thing has been done among you

This can be stated in active form. Alternate translation: "that the people of the city have done such a terrible thing" (See: rc://en/ta/man/jit/figs-activepassive)