
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 \(a, b, c, x, y, z \in \mathbf{R}_{+}\) satisfying the equations:
\[
cy + bz = a, \quad az + cx = b, \quad bx + ay = c,
\]
find the minimum value of the function
\[
f(x, y, z) = \frac{x^2}{1 + x} + \frac{y^2}{1 + y} + \frac{z^2}{1 + z}.
\]

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