
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
Consider the set of numbers $\{8, 88, 888, 8888, \ldots, 888888888\}$. Calculate the arithmetic mean, denoted as $N$, of these nine numbers. $N$ is an $8$-digit number, and all of its digits are distinct. Identify which of the following digits does not appear in $N$.
A) 3
B) 4
C) 5
D) 6
E) 0

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