
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 numbers \( a, b, c, x, y, z \) such that \( cy + bz = a \), \( az + cx = b \), and \( bx + ay = c \), 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