
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
For all positive integers from 1 to 1,000,000,000, calculate the sum of the digits of each number. Then, for those resulting numbers, calculate the sum of their digits, and so on until all resulting numbers are single digits. Determine whether the digit 1 appears more frequently than the digit 2 among these single-digit results.


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