
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
The unknown real numbers \(x, y, z\) satisfy the equations
\[
\frac{x + y}{1 + z} = \frac{1 - z + z^2}{x^2 - xy + y^2}
\]
\[
\frac{x - y}{3 - z} = \frac{9 + 3z + z^2}{x^2 + xy + y^2}.
\]

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