
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 \( x, y, z \) satisfying \( xyz = 1 \), find the maximum value of \( f(x, y, z) = (1 - yz + z)(1 - xz + x)(1 - xy + y) \) and the corresponding values of \( x, y, z \).

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