Let $a , b , c$ be real numbers and $0 < b < 1$ such that
$$\begin{aligned}
& a = b \cdot c \\
& a + c = b
\end{aligned}$$
Given this, which of the following orderings is correct?\\
A) $a < b < c$\\
B) $a < c < b$\\
C) $b < a < c$\\
D) $c < a < b$\\
E) $c < b < a$