
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 hundreds digit of each term is the tens digit of the next term, the tens digit of each term is the units digit of the next term, and the units digit of each term is the hundreds digit of the next term, in that sequence, looping back at the end. For example, the sequence might begin with the terms 123, 231, 312. Given that $S$ is the sum of all the terms in the sequence, what is the largest prime factor that always divides $S$?
A) 3
B) 7
C) 13
D) 37
E) 43

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