
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 \( n \) be a fixed positive integer. Find the maximum possible value of
\[ 
\sum_{1 \leq r < s \leq 2n} (s - r - n) x_r x_s,
\]
where \( -1 \leq x_i \leq 1 \) for all \( i = 1, 2, \ldots, 2n \).

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