设集合 $A=\left\{\right(x,y\left)\right|\frac{m}{2}\le (x-2{)}^2+y^2\le m^2,x,y\in R\}$, $B=\left\{\right(x,y\left)\right|2m\le x+y\le 2m+1,x,y\in R\}$若 $A\cap B\ne \varphi$则实数 $m$的取值范围是.