
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
Joãozinho wrote the numbers from 1 to 100000 on the board, then replaced each number by the sum of its digits and repeated this process until he obtained a list of 100000 single-digit numbers. For example, starting with the number 7234, we get \(7+2+3+4=16\) and \(1+6=7\).

(a) What number replaced the number 98765?

(b) How many times does the number 8 appear in the final list?

(c) Which number appears the most times?

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