在矩形 $ABCD$中,边 $AB,AD$的长分别为2,1.若 $M,N$分别是边 $BC,CD$上的点，且满足 $\frac{\left|\stackrel{\rightharpoonup }{BM}\right|}{\left|\stackrel{\rightharpoonup }{BC}\right|}=\frac{\left|\stackrel{\rightharpoonup }{CN}\right|}{\left|\stackrel{\rightharpoonup }{CD}\right|}$.则 $\stackrel{\rightharpoonup }{AM}·\stackrel{\rightharpoonup }{AN}$的取值范围是.