HMMT November 2021 H6

Let $n$ be the answer to this problem. $a$ and $b$ are positive integers satisfying

$$\begin{aligned} & 3 a+5 b \equiv 19 (\bmod n+1) \\ & 4 a+2 b \equiv 25 (\bmod n+1) \end{aligned}$$

Find $2 a+6 b$.