Alice, Bob, and Charlie were trying to estimate the number of marbles in a jar. When Alice said, "There are at least $80$ marbles," Bob replied, "There are at most $75$ marbles." Charlie then remarked, "Actually, there are at most $70$ marbles." It turned out that none of the three statements were true. Let $M$ be the actual number of marbles in the jar. Which of the following intervals is the set of all possible values of $M$?