
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

The magician taught Kashtanka to bark the number of times he secretly showed her. When Kashtanka correctly answered how much two times two is, he hid a delicious cake in a suitcase with a combination lock and said:

- The eight-digit code for the suitcase is the solution to the puzzle УЧУЙ $=\text{KE} \times \text{KS}$. You need to replace the same letters with the same digits and different letters with different digits so that the equality is true. Bark the correct number of times for each of the eight characters, and you will get the treat.

But then there was a confusion. Kashtanka, out of excitement, barked 1 more time for each letter than she should have. Of course, the suitcase did not open. Suddenly, a child's voice said: "It's not fair! The dog solved the puzzle correctly!" And indeed, if each digit of the solution the magician had in mind is increased by 1, another solution to the puzzle emerges!

Is it possible to determine: a) what exact solution the magician had in mind; b) what the value of the number УЧУЙ was in that solution?

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