
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
On an infinite tape, numbers are written in a row. The first number is one, and each subsequent number is obtained by adding the smallest non-zero digit of its decimal representation to the previous number. How many digits are in the decimal representation of the number that is in the $9 \cdot 1000^{1000}$-th place in this sequence?

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