
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
\[
\begin{cases}
x^2 - 3y + z = -4 \\
x - 3y + z^2 = -10 \\
3x + y^2 - 3z = 0
\end{cases}
\]

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