Let $p(x)$ be the density function given by $$p(x) = \begin{cases} \frac{2}{154}x & \text{if} \;\; 0\leq x \leq 7\\ \frac{2}{15} - \frac{2}{330}x & \text{if} \;\; 7 \leq x \leq 22\\ 0 & \text{otherwise.} \end{cases}$$ Find the mean value of $p(x)$.