An electronic device displays a user interface that includes one or more user interface elements; detects a user input on a touch-sensitive surface that includes detecting a contact at a location that corresponds to a respective user interface element; and, in response: if the user input satisfies menu-display criteria, including a criterion that is satisfied when the contact has an intensity above a first intensity threshold, displays a first menu overlaid on the user interface; and, if the user input satisfies action criteria, wherein the action criteria are capable of being satisfied when the intensity of the contact is below the first intensity threshold, initiates performance of an action associated with the respective user interface element without displaying the first menu.