
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
Determine the maximum value of the sum
\[ \sum_{i < j} x_ix_j (x_i \plus{} x_j)
\]
over all  $ n \minus{}$ tuples  $ (x_1, \ldots, x_n),$  satisfying  $ x_i \geq 0$  and  $ \sum^n_{i \equal{} 1} x_i \equal{} 1.$ 

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