
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  $x_1 , x_2 ,\ldots, x_n$  be real numbers in  $[0,1].$  Determine the maximum value of the sum of the  $\frac{n(n-1)}{2}$  terms:  $$ \sum_{i<j}|x_i -x_j |. $$  

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