
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  $\left(x,\ y,\ z\right)$  of integers satisfying the following system of equations:

 $x^3-4x^2-16x+60=y$ ;
 $y^3-4y^2-16y+60=z$ ;
 $z^3-4z^2-16z+60=x$ .

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