
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 numbers \( x, y, z \) satisfying the system of equations:

$$
\left\{
\begin{array}{l}
(x+1) y z = 12 \\
(y+1) z x = 4 \\
(z+1) x y = 4
\end{array}
\right.
$$

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