Interval containing the limit of the sample mean

Let $\{X_n\}_{n\ge1}$ be a sequence of i.i.d. random variables with the probability mass function

$$f(x)=\begin{cases}\frac14, & x=4,\ \frac34, & x=8,\ 0, & \text{otherwise.}\end{cases}$$

Let $\overline X_n=\frac1n\sum_{i=1}^nX_i$, $n=1,2,…$. If $\lim_{n\to\infty}P(m\le\overline X_n\le M)=1$, then possible values of $m$ and $M$ are