已知向量\(\overrightarrow{α}{\rm=}({\rm-}1,{\rm-}1)\)、\(\overrightarrow{\beta}\text{=}\left(0,1\right).\)

\((1)\)若向量\(\left(t\overrightarrow{\alpha}+\overrightarrow{\beta}\right)//\left(\overrightarrow{\alpha}+t\overrightarrow{\beta}\right)\)，求实数\(t\)的值；

\((2)\)若向量\(\overrightarrow{c}=\left(x,y\right)\)满足\(\overrightarrow{c}=-y\cdot\overrightarrow{\alpha}+\left(1-x\right)\overrightarrow{\beta}\)，求\(\left|\overrightarrow{c}\right|\)的值．