
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 series of three-digit numbers is structured such that the last two digits (tens and units) of each number become the first two digits (hundreds and tens) of the subsequent number, and the series loops such that the last two digits of the final number in the series become the first two digits of the first number. Given a series that starts with 368, 689, and ends with 836, calculate the largest prime factor that consistently divides the sum of all numbers in this series.
- **A)** 3
- **B)** 7
- **C)** 13
- **D)** 31
- **E)** 37

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