
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 positive real numbers \(x\), \(y\), and \(z\) that satisfy the following system of equations:
\[
\begin{aligned}
x^{2}+y^{2}+x y &= 1, \\
y^{2}+z^{2}+y z &= 4, \\
z^{2}+x^{2}+z x &= 5,
\end{aligned}
\]
find \(x+y+z\).

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