阅读理解。

 Dear Mum,

    Thanks for the new dress. It's so nice! It's hot in Wuhan. I wear the dress to school. I am very happy. Miss Li says I can go back home after Friday. I want to buy a pair of sunglasses.They'reninety-one yuan. Thet're too expensive.

                                                                                                                                                                                              Love,Mary

已知O为△ABC的外心，|$\overrightarrow{AB}$|=16，|$\overrightarrow{AC}$|=10$\sqrt{2}$，若$\overrightarrow{AO}$=x$\overrightarrow{AB}$+y$\overrightarrow{AC}$，且32x+25y=25，则|$\overrightarrow{AO}$|=____ 

同学们在进行比较水和沙子的吸热能力的探究实验．