
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
In the game "set," all possible four-digit numbers consisting of the digits 1, 2, and 3 (each digit used exactly once) participate. A triplet of numbers is said to form a set if, for each digit position, either all three numbers have the same digit, or all three numbers have different digits.

The difficulty of a set is defined as the number of digit positions where all three digits are different.

For example:
- The numbers 1232, 2213, and 3221 form a set of difficulty 3 (in the first position all three digits are different, in the second position only the digit 2 is present, in the third position all three digits are different, and in the fourth position all three digits are different).
- The numbers 1231, 1232, and 1233 form a set of difficulty 1 (in the first three positions the digits are the same, and only in the fourth position all three digits are different).
- The numbers 1123, 2231, and 3311 do not form a set at all (in the last position there are two ones and one three).

Which difficulty level sets are most numerous in the game and why?

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