
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 real solutions \((x, y, z)\) of the system of equations
$$
\left\{\begin{array}{l}
3\left(x^{2}+y^{2}+z^{2}\right)=1, \\
x^{2} y^{2}+y^{2} z^{2}+z^{2} x^{2}=x y z(x+y+z)^{2}
\end{array}\right.
$$.

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