
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
Calculate the arithmetic mean \( M \) of the numbers in the set \(\{1, 22, 333, 4444, \ldots, 999999999\}\), each component-wise containing repeated digits starting from '1' to '9' where the first number '1' has one digit, second number '22' has two digits, and so on up to '999999999' comprising nine digits in total. Determine which digit from 0 to 9 does not appear in the computed arithmetic mean \( M \).

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