
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 integer solutions to the system of equations:
\begin{align*}
xy + yz + zx &= -4 
x^2 + y^2 + z^2 &= 24 
x^{3} + y^3 + z^3 + 3xyz &= 16
\end{align*}

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