Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$, respectively. A right angled triangle $AMN$ is inscribed in the triangle $O A B$, where $O$ is the origin and the points $M$ and $N$ lie on the lines $O B$ and $AB$, respectively. If the area of the triangle AMN is $\frac{4}{9}$ of the area of the triangle $OAB$ and $AN$ : $N B=\lambda: 1$, then the sum of all possible value(s) of is $\lambda:$