
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
Find all \((x, y, z)\) such that:

\[
\left\{\begin{array}{c}
x + y + z = \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \\
x^2 + y^2 + z^2 = \frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}
\end{array}\right.
\]

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