
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
If a three-digit number is written twice consecutively, the resulting number is divided by 7, the quotient obtained is divided by 11, and the new quotient is divided by 13, we get the original number again. Why?

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