
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 \( a, b, c \) be non-negative real numbers such that \( a + b + c = 3 \).

Find the maximum value of \( S = \left(a^{2} - ab + b^{2}\right)\left(b^{2} - bc + c^{2}\right)\left(c^{2} - ca + a^{2}\right) \).

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