
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 finite sequence of four-digit integers has the property that the hundreds, tens, and units digits of each term become, respectively, the thousands, hundreds, and tens digits of the next term, while the thousands digit of each term becomes the units digit of the next term. For example, one such sequence could be 2478, 4782, 7824, and 8247. Let $T$ be the sum of all the terms in the sequence. What is the largest prime factor that always divides $T$?
A) 5
B) 7
C) 11
D) 13
E) 101

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