You 'stoop down' or 'lean down' to tie your shoes?

Or you could kneel down, squat down or sit down to do it.

I think we normally bend down to do that. "Stoop" and "lean" are odd.

A book's question: The schoolboy _____down to tie his shoelace.
a.stooped b.leaned c.turned d.went

The free dictionary.com:
Stoop down: to dip, duck, or squat down. I had to stoop down to enter the tiny door. Stoop down so you don't bump your head.
Lean down: to bend over. Lean down and tie your shoe before you trip. He leaned down and picked something up from the floo

The test writer wanted 'stooped', I think, but 'leaned' is possible, too.