
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
12 balls numbered 1 through 12 are placed in a bin. Joe produces a list of three numbers by performing the following sequence three times: He chooses a ball, adds 5 to the number of the ball, records the new number, and places the ball back in the bin. How many different lists are possible, considering the numbers continue from 1 after reaching 12 (i.e., ball 12 + 5 -> becomes 5)?

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