
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
Consider a two-digit number in base 12 represented by $AB_{12}$, where $A$ and $B$ are duodecimal digits (0 to 11), and $A \neq B$. When this number is reversed to $BA_{12}$, under what condition is a particular prime number a necessary factor of the difference $AB_{12} - BA_{12}$?

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