
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
Determine all triples  $(x,y,z)$  of integers greater than  $1$  with the property that  $x$  divides  $yz-1$ ,  $y$  divides  $zx-1$  and  $z$  divides  $xy-1$ .

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