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.

Why should the mean inequalities not work? Geometric mean vs. mean of power 4
$$
abc\le\left(\frac{a^4+b^4+c^4}3\right)^{\frac34}
$$and arithmetic mean vs. mean of power 4$$
\frac{a+b+c}3\le\left(\frac{a^4+b^4+c^4}3\right)^{\frac14}
$$
implies
$$
\frac{abc(a+b+c)}3\le \frac{a^4+b^4+c^4}3.
$$
