
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
Let positive numbers \( x \), \( y \), and \( z \) satisfy the system of equations:

\[ 
\left\{\begin{array}{l}
x^{2}+xy+y^{2}=147 \\
y^{2}+yz+z^{2}=9 \\
z^{2}+xz+x^{2}=156
\end{array}\right.
\]

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

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