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Since you have Implanon (and not the birth control pills) for birth control, you can start on diet pills. Diet pills (depending on their mechanism of action and composition) are known to affect the efficacy of the oral contraceptive pills by affecting their absorption. However, since all birth control methods are associated with failures, consider using additional protection while having intercourse especially while being on the diet pills. For further clarification and discussion visit your gynecologist/obstetrician.
Take care.