
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 sequence of four-digit integers where the hundreds, tens, and units digits of each term are, respectively, the thousands, hundreds, and tens digits of the next term, and the hundreds, tens, and units digits of the last term are, respectively, the thousands, hundreds, and tens digits of the first term. For instance, a sequence could start with 1638, 6381, 3816, 8163, and end with 1638 again. Let \( T \) represent the sum of all terms in this sequence. Determine the largest prime factor that always divides \( T \).
A) 11
B) 37
C) 101
D) 407

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