
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
Given \( x, y, z \in \mathbf{Z} \) such that \(\left\{\begin{array}{l}x+ y + z = 3 \\ x^3 + y^3 + z^3 = 3\end{array}\right.\), determine the set of all possible values of \( x^2 + y^2 + z^2 \).

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