Dice Deception

Alice and Bob are playing a board game. On their turn, a player must roll $N$ standard $6$-sided dice, and their action will be determined by the sum of values on the top faces of the $N$ dice. On a certain turn of Alice, she rolls the dice and obtains the sequence of values $A_1, A_2, \ldots, A_N$ on the top faces. However, Bob isn't paying attention, allowing Alice to cheat a little! Alice