
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 three-digit integers is defined such that the tens and units digits of each term become the hundreds and tens digits of the next term, and the hundreds digit of each term becomes the units digit of the next term. The sequence cycles such that the tens, units, and hundreds digits of the last term cycle back to form the hundreds, tens, and units digits of the first term, respectively. Let $T$ be the sum of all terms in this sequence. Determine the largest prime factor that always divides $T$.
A) 3
B) 7
C) 13
D) 37
E) 43

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