3 Let $F(x)=|f(x) \cdot g(x)|$, where $f(x)=a x^{2}+b x+c, x \in[-1,1]$; $g(x)=c x^{2}+b x+a, x \in[-1,1]$, and for any parameters $a, b, c$, it always holds that $|f(x)| \leqslant 1$. Find the maximum value of $F(x)$.