For positive real numbers $a,b,c$ prove that $ a^4 + b^4 + c^4 \ge abc(a+b+c)$ For positive reals $a,b,c$ prove that $$ a^4+b^4+c^4 \ge abc(a+b+c). $$
I tried to pls around trying to reorganize to get AM-GM but i couldn't 
Thanks for the help in advance.

Hint
$$\frac{a^4+a^4+b^4+c^4}{4}\geq abca \\
\frac{a^4+b^4+b^4+c^4}{4}\geq abcb \\
\frac{a^4+c^4+b^4+c^4}{4}\geq abcc \\$$
