已知 $\alpha_1, \alpha_2, \alpha_3, \beta, \gamma$ 均是 4 维列向量，又 $A=\left(\alpha_1, \alpha_2, \alpha_3, \beta\right), B=\left(\alpha_1, \alpha_2, \alpha_3, \gamma\right)$ ，若 $|\boldsymbol{A}|=3,|\boldsymbol{B}|=2$ ，求 $|\boldsymbol{A}+2 \boldsymbol{B}|$ ．