15. Let $m>0$, if for any set of positive numbers $a, b, c$ satisfying $a b c \leqslant \frac{1}{4}$ and $\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}<m$, there always exists a triangle with side lengths $a, b, c$, find the maximum value of the real number $m$, and explain the reason.