
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 for \( x, y, z \in \mathbb{R}^{+} \) (positive real numbers) the following system of equations:

\[ 
x y + y z + z x = 12
\]

\[
x y z = 2 + x + y + z
\]

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