The coordinates of a dot $$P$$ moving in the $$xy$$ plane at time $$t$$ are given by: $$x = 5e^{-t}\cos t$$ and $$y = 5e^{-t} \sin t$$. Let $$L_a$$ be the distance traveled by $$P$$ in the interval $$0 \leq t \leq a$$. If $$\displaystyle \lim_{a \to \infty} L_a = z$$, what is the value of $$z^2$$?