
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 nine-digit natural number \(A\), written in the decimal system, is obtained from a number \(B\) by moving its last digit to the first position. It is known that the number \(B\) is coprime with the number 24 and \(B > 666666666\). Find the largest and smallest numbers \(A\) that satisfy these conditions. (Two natural numbers are coprime if they have no common divisors other than one).

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