
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 all triples  $ (x,y,z)$  of integers which satisfy

 $ x(y \plus{} z) \equal{} y^2 \plus{} z^2 \minus{} 2$ 

 $ y(z \plus{} x) \equal{} z^2 \plus{} x^2 \minus{} 2$ 

 $ z(x \plus{} y) \equal{} x^2 \plus{} y^2 \minus{} 2$ .

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