Circle $ O$ is inscribed in a trapzoid $ ABCD$, $ \angle{A}$ and $ \angle{B}$ are all acute angles. A line through $ O$ intersects $ AD$ at $ E$ and $ BC$ at $ F$, and satisfies the following conditions: (1) $ \angle{DEF}$ and $ \angle{CFE}$ are acute angles. (2) $ AE+BF=DE+CF$. Let $ AB=a$, $ BC=b$, $ CD=c$, then use $ a,b,c$ to express $ AE$.