I set down my backpack in the hallway when I get home.
Notice that the transitive verb (the one you do to an object) is more regular than the intransitive verb (the one you do to yourself). Set adds -ing to the present progressive, but the present, past, and past progressive are the same. Sit adds -ing, but changes to sat in the past and past progressive.
I sit down on my bed when I am tired.
I am sitting down on my bed right now.
I sat down on my bed yesterday.
In the past I have sat down on my bed.
I set my backpack down in the hall.
I am setting my backpack down.
Yesterday I set my backpack down.
In the past I have set my back pack down.
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