
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
 $\mathbb{Q}$  is set of all rational numbers. Find all functions  $f:\mathbb{Q}\times\mathbb{Q}\rightarrow\mathbb{Q}$  such that for all  $x$ ,  $y$ ,  $z$   $\in\mathbb{Q}$   satisfy  $f(x,y)+f(y,z)+f(z,x)=f(0,x+y+z)$ 

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