
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
Suppose 3 distinct numbers are chosen from \(1, 2, \ldots, 3n\) with their sum equal to \(3n\). What is the largest possible product of those 3 numbers? 
(a) \(n^{3}-n\);
(b) \(n^{3}\);
(c) \(n^{3}+n\);
(d) \(n^{3}-7n+6\);
(e) \(n^{3}-7n-6\).

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