
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 a game called "set," all possible four-digit numbers consisting of the digits 1, 2, and 3 (each used exactly once) are considered. A triplet of numbers forms a set if for each digit position, either all three numbers have the same digit, or all three numbers have different digits.

For example, the numbers 1232, 2213, 3221 form a set because in the first position, all three digits (1, 2, and 3) are present; in the second position, only the digit 2 is present; in the third position, all three digits are present; and in the fourth position, all three digits are present. The numbers 1123, 2231, and 3311 do not form a set because in the last position there are two 1s and a 3.

How many total sets exist in the game?

(Note: Rearranging the numbers does not create a new set. For instance, 1232, 2213, and 3221 is considered the same set as 2213, 1232, and 3221.)

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