
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 each number from 1 to 1,000,000,000, the sum of its digits is calculated. For each of the resulting one billion numbers, the sum of its digits is calculated again, and so on, until there is a billion single-digit numbers. Which digit will appear more frequently: 1 or 2?

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