[不等式] Hard one.

Let $ a,b,c \geq 0$ prove that:
\[  \frac{a^{2}+b^{2}+c^{2}}{ab+bc+ca}+\frac{69(a^{3}b+b^{3}c+c^{3}a)}{(a+b+c)^{4}}\ge\frac{32}{9} \]


Ps: 好久没上了。busy in school exam...