
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
A sequence of four-digit integers has the property that 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 example, such a sequence might begin with the terms 2478, 4785, 7852, and 8524. Let $T$ be the sum of all the terms in the sequence. What is the largest prime factor that always divides $T$?
A) 11
B) 37
C) 101
D) 111
E) 999

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