
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
Compute all ordered triples \((x, y, z)\) of real numbers satisfying the following system of equations:
\[ 
\begin{array}{r}
xy + z = 40 \\
xz + y = 51 \\
x + y + z = 19.
\end{array}
\]

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