
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 
\[
(x^3 - xy^2 + y^3)(x^3 - xz^2 + z^3)(y^3 - yz^2 + z^3).
\]

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