
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 special sequence of four-digit integers has the property that the hundreds, tens, and units digits of each term are, respectively, the thousands, hundreds, and tens digits of the next term, and the hundreds, tens, and units digits of the last term are, respectively, the thousands, hundreds, and tens digits of the first term. If the sequence begins with the numbers 3546, 5468, 4683, and ends with 6835, calculate the sum of all the numbers in the sequence and determine the largest prime factor that always divides the sum.
A) 3
B) 11
C) 37
D) 101
E) 9999

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