
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

Given that the positive numbers \(x, y, z\) satisfy the system of equations:

\[
\left\{\begin{array}{l}
x^{2} + xy + y^{2} = 12 \\
y^{2} + yz + z^{2} = 25 \\
z^{2} + xz + x^{2} = 37
\end{array}\right.
\]

find the value of the expression \(xy + yz + xz\).

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