Let $a, b, c, d, e$ be real numbers satisfying the following conditions:
\[
\begin{align*}
& a \le b \le c \le d \le e, \\
& a + e = 1, \\
& b + c + d = 3, \\
& a^2 + b^2 + c^2 + d^2 + e^2 = 14
\end{align*}
\]
Determine the maximum possible value of $ae$.

Let's think step by step and output the final answer within \boxed{}.
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