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

\[
\begin{cases}
x^2 + xy + y^2 = 27 \\
y^2 + yz + z^2 = 9 \\
z^2 + xz + x^2 = 36
\end{cases}
\]

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

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