
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
a) How many 1-digit, 2-digit, 3-digit, and generally $n$-digit numbers are there?

b) How many digits do we need if we want to write all natural numbers from 1 to $10^n$ (not including $10^n$)?

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