
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 for integers  $x,y,z$ : \[ \{ \begin{array}{ccc} x + y &=& 1 - z  x^3 + y^3 &=& 1 - z^2 . \end{array}  \]

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