
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
Solve the system of equations: 
\[
\left\{
\begin{array}{l}
x^{3}+y^{3}=3 y+3 z+4, \\
y^{3}+z^{3}=3 z+3 x+4, \\
z^{3}+x^{3}=3 x+3 y+4
\end{array}
\right.
\]

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