"Nothing, thank you."
De nada means "your welcome" (if you're translating it literally it means "of nothing"). Nada itself means nothing (it's also formal version of the verb you swim). If you were to say "de nada, gracias", you would be saying "you're welcome, thank you".
That would be no thank you not nothing thank you essentially it is situational..
So if someone said would you like anything you would use nada gracias.. you wouldn't use no gracias if some else you would you like would you like for example coffee.