Find the number of the fixed point of $G^n$ if we define $G(x)=4x(1-x)$ and $G:[0,1] \to [0,1]$

Question

Let $G:[0,1] \to [0,1]$ and $G(x)=4x(1-x)$.

Find the number of the fixed points of $G^n$ with $n \geq 1$.

It is easy to find the number of the fixed points if $n=1,2$, or even $3$ using equation $G(x)=x$. But I don't know how to calculate for the general case n. If someone can help me with this, it would be very appreciated. Thank you.