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

\[
\begin{cases}
x^2 + y^2 + xy = 3, \\
y^2 + z^2 + yz = 4, \\
z^2 + x^2 + zx = 7.
\end{cases}
\]

Find the value of \( x + y + z \).

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