
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  $(a_1,\ldots,a_{20})$  and  $(b_1,\ldots,b_{20})$  are two sequences of integers such that the sequence  $(a_1,\ldots,a_{20},b_1,\ldots,b_{20})$  contains each of the numbers  $1,\ldots,40$  exactly once.  What is the maximum possible value of the sum \[\sum_{i=1}^{20}\sum_{j=1}^{20}\min(a_i,b_j)?\]

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