
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 three-digit integers has the property that the units digit of each term becomes the hundreds digit of the next term, and the tens and hundreds digits of each term become respectively the units and tens digits of the next term. The sequence cycles such that the digits of the last term follow the same rule to form the first term. For example, a sequence could start with 247, resulting in the next terms being 472 and 724, and cycling back to 247. Let $T$ be the sum of all the terms in the sequence. What is the largest prime factor that always divides $T$?
A) 3
B) 7
C) 13
D) 37
E) 43

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