
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
Consider a sequence of four-digit integers where each integer's last three digits are, respectively, the first three digits of the subsequent integer, and the sequence is cyclic (the last three digits of the last integer are the first three digits of the first integer). For instance, the sequence might begin with 1203, 2037, and 3720, ending with 7201. Define $T$ as the sum of all integers in the sequence. Determine the largest prime factor that consistently divides $T$.
A) 3
B) 7
C) 13
D) 37
E) 43

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