
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
Find the functions  $f:\mathbb{Z}\times \mathbb{Z}\to\mathbb{R}$  such that

a)  $f(x,y)\cdot f(y,z) \cdot f(z,x) = 1$  for all integers  $x,y,z$ ;

b)  $f(x+1,x)=2$  for all integers  $x$ .

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