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

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