
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 \( x, y, z \in \mathbb{R}_+ \), and 

\[ x^2 + y^2 + xy = 1, \]
\[ y^2 + z^2 + yz = 2, \]
\[ z^2 + x^2 + zx = 3, \]

find \( x + y + z \).

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