$\definecolor{A}{RGB}{190,0,60}\color{A}\fbox{A1.}$ Find all $f:\mathbb{R}\rightarrow \mathbb{R}$ such that $$\definecolor{A}{RGB}{80,0,200}\color{A} x^4+y^4+z^4\ge f(xy)+f(yz)+f(zx)\ge xyz(x+y+z)$$holds for all $a,b,c\in\mathbb{R}$.

[i]Proposed by [/i][b][color=#FFFF00]usjl[/color][/b].
[color=#B6D7A8]#1733[/color]