
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 follows the rule that the last three digits of each number become the first three digits of the next number, and the last three digits of the last number become the first three digits of the first number. For instance, a sequence might start with 1301, followed by 0130, and so on until it ends with a number whose last three digits are 130. If $S$ represents the sum of all terms in this sequence, find the largest prime factor that consistently divides $S$.
A) 11
B) 37
C) 101
D) 123
E) 202

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