
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 \(x,\) \(y,\) and \(z\) be nonnegative real numbers such that \(x + y + z = 3.\) Find the maximum value of 
\[
(x^2 - xy + y^2)(y^2 - yz + z^2)(z^2 - zx + x^2)
\]

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