
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 that \(\left(a_{1}, \ldots, a_{20}\right)\) and \(\left(b_{1}, \ldots, b_{20}\right)\) are two sequences of integers such that the sequence \(\left(a_{1}, \ldots, a_{20}, b_{1}, \ldots, b_{20}\right)\) contains each of the numbers \(1, \ldots, 40\) exactly once. What is the maximum possible value of the sum
\[
\sum_{i=1}^{20} \sum_{j=1}^{20} \min \left(a_{i}, b_{j}\right) ?
\]

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