8. Let the focus of the parabola $C: y^{2}=4 x$ be $F$, and let the line $L$ passing through point $F$ intersect $C$ at points $P, Q$. Suppose $L$ intersects the directrix of parabola $C$ at point $M$, and $\overrightarrow{F M}=3 \overrightarrow{F P}$, then $|\overrightarrow{F P}|=$ $\qquad$ .
As shown in the figure, if $P, M$ are on the same side of the $x$-axis, then $\frac{|M P|}{|M F|}=\frac{2}{3}$ $\Rightarrow|P N|=\frac{2}{3}|F K|=\frac{4}{3}$, at this time $|\overrightarrow{F P}|=\frac{4}{3}$; if $P, M$ are on opposite sides of the $x$-axis, then $\frac{|M F|}{|M P|}=\frac{3}{4}$ $\Rightarrow|F K|=\frac{3}{4}|P N| \Rightarrow|P N|=\frac{8}{3}$, at this time $|\overrightarrow{F P}|=\frac{8}{3}$. In summary, $|\overrightarrow{F P}|=\frac{4}{3}$ or $\frac{8}{3}$.