
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 integer solutions of the system of equations
$$
\left\{\begin{array}{l}
x^{3}-4 x^{2}-16 x+60=y \\
y^{3}-4 y^{2}-16 y+60=z \\
z^{3}-4 z^{2}-16 z+60=x
\end{array}\right.
$$.

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