
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 \( a_{1}, a_{2}, \ldots, a_{2000} \) be real numbers in the interval \([0,1]\). Find the maximum possible value of
\[ 
\sum_{1 \leq i < j \leq 2000}(j - i) \left| a_{j} - a_{i} \right| 
\]

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