
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 \(a, b, c, d, e, f\) be non-negative real numbers satisfying \(a + b + c + d + e + f = 6\). Find the maximal possible value of

\[
a b c + b c d + c d e + d e f + e f a + f a b
\]

and determine all 6-tuples \((a, b, c, d, e, f)\) for which this maximal value is achieved.

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