
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
An eight-digit natural number \( A \), written in the decimal system, is obtained from the number \( B \) by moving its last digit to the first position. It is known that the number \( B \) is coprime with 36 and \( B > 77,777,777 \). Find the largest and smallest numbers \( A \) that satisfy these conditions. (Two natural numbers are called coprime if they have no common divisors other than one).

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