A random variable $X$ follows a normal distribution $\mathrm{N}\left(m_{1}, \sigma_{1}^{2}\right)$ and a random variable $Y$ follows a normal distribution $\mathrm{N}\left(m_{2}, \sigma_{2}^{2}\right)$, satisfying the following conditions. For all real numbers $x$, $\mathrm{P}(X \leq x) = \mathrm{P}(X \geq 40 - x)$ and $\mathrm{P}(Y \leq x) = \mathrm{P}(X \leq x + 10)$. When $\mathrm{P}(15 \leq X \leq 20) + \mathrm{P}(15 \leq Y \leq 20) = 0.4772$ using the standard normal distribution table below, what is the value of $m_{1} + \sigma_{2}$? (Given: $\sigma_{1}$ and $\sigma_{2}$ are positive.) [4 points]
| $z$ | $\mathrm{P}(0 \leq Z \leq z)$ |
| 0.5 | 0.1915 |
| 1.0 | 0.3413 |
| 1.5 | 0.4332 |
| 2.0 | 0.4772 |