
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
Let \( x, y, z \in \mathbf{R}^{+} \) and \( x^{2} + y^{2} + z^{2} = 1 \). Find the minimum value of
\[ \frac{x^{5}}{y^{2} + z^{2} - y z} + \frac{y^{5}}{z^{2} + x^{2} - z x} + \frac{z^{5}}{x^{2} + y^{2} - x y} .\]

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