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Latin word reflectere comes from Latin flecto, Latin re-, and later Latin reflecto (I reflect. I turn back or away.)
flecto (Latin)
(figuratively) I persuade, prevail upon, or soften. I bend, curve or bow. I turn or curl.
re- (Latin)
Again; prefix added to various words to indicate an action being done again, or like the other usages indicated above under English.. Back, backwards.
reflecto (Latin)
I reflect. I turn back or away.