
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:

$$
\begin{cases}
x^{2}+y^{2}+x y=529 \\
x^{2}+z^{2}+\sqrt{3} x z=441 \\
z^{2}+y^{2}=144
\end{cases}
$$

Find the value of the expression \(\sqrt{3} x y + 2 y z + x z\).

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