
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 units and tens digits of each term are, respectively, the tens and hundreds digits of the next term, and the units and tens digits of the last term are, respectively, the tens and hundreds digits of the first term. The sequence consists of four terms. Let $S$ be the sum of all the terms in the sequence. What is the largest prime factor that always divides $S$?
A) 2
B) 3
C) 5
D) 7
E) 11

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