
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

Carlinhos likes writing numbers in his notebook. One day he wrote the numbers from 1 to 999, one after the other, to form the giant number:

$$
123456789101112 \ldots 997998999
$$

Based on this number, the following questions are asked:

(a) How many digits were written?

(b) How many times does the digit 1 appear?

(c) Considering that 1 occupies position 1, 2 occupies position 2, and 0 appears for the first time occupying position 11, which digit occupies position 2016?

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