
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 has the property that the hundreds, tens, and units digits become, respectively, the thousands, hundreds, and tens digits of the next term, and the hundreds, tens, and units digits of the last term become, respectively, the thousands, hundreds, and tens digits of the first term. Find the largest prime factor that always divides the sum of all the terms in the sequence.

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