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The method for calculating the average of the nearest repeated numbers in a list is:

1. Identify all the repeated numbers in the list.
2. Calculate the difference between the indices of each pair of adjacent repeated numbers.
3. Take the minimum of these differences, which represents the distance between the nearest repeated numbers.
4. Select all the pairs of adjacent repeated numbers that have the minimum distance between them.
5. For each pair, calculate the average of the two numbers.
6. Calculate the average of all the averages obtained in step 5.

This final result represents the average of the nearest repeated numbers in the list.