
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
 $\definecolor{A}{RGB}{190,0,60}\color{A}\fbox{A1.}$  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  $a,b,c\in\mathbb{R}$ .

*Proposed by***<span style="color:#FFFF00">usjl</span>**.
<span style="color:#B6D7A8">#1733</span>

Present the answer in LaTex format: \boxed{Your answer}
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