
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 as many times as he secretly showed her. When Kashtanka correctly answered how much two times two is in this way, he hid a delicious cake in a suitcase with a combination lock and said:

"The eight-digit code to the suitcase is the solution to the puzzle УЧУЙ $=\kappa \mathrm{E} \times$ КС. You need to replace identical letters with identical digits and different letters with different digits so that it results in a correct equation. Bark the needed number of times for each of the eight letters, and you will get a treat."

But then something went wrong. Kashtanka, out of excitement, barked one more time than needed for each letter. The suitcase, of course, did not open. Suddenly a child's voice exclaimed: "Unfair! The dog solved the puzzle correctly!" And indeed, if each digit in the magician's intended solution is increased by 1, it results in another solution to the puzzle!

Can we determine:
a) What exactly was the solution intended by the magician?
b) What was the number УЧУЙ in this solution?
[7 points] (A. K. Kulggin, T. A. Korchemkina, I. V. Raskina)

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