
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 value of   $$ \frac{1}{1+x+xy}+\frac{1}{1+y+yz}+\frac{1}{1+z+zx} $$   if  $x$ ,  $y$  and  $z$  are real numbers usch that  $xyz=1$ 

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