The correct answer is wisely. The phrase "you can only pick one" establishes the constraint, while "choose wisely" is the instruction on how to make that single selection. By choosing "wisely," you are acknowledging and following the instruction to pick one, making the selection itself the "wise" choice.
"You can only pick one": This part of the phrase sets a rule, not a choice. It dictates that the final answer can only be a single word.
"Choose wisely": This part is the instruction on how to fulfill the rule. It is an adverb telling you how to make your choice, so the correct response is the word that represents the action of choosing wisely... yeah