Loci From Foci

Two points $F_1,F_2$ and a point $P$ satisfy that $|F_1P-F_2P|=2$ and $F_1F_2=4$ . Let $I$ be the incenter of $\triangle F_1PF_2$ . As $P$ varies, $I$ traces out two disjoint loci. What is the sum of the lengths of these two loci? Round to the nearest thousandths.

$\text{Details and Assumptions}$

The incircle is drawn inaccurately on purpose.