
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
At what frequency does the digit 7 appear in the decimal representation of natural numbers? That is, find the limit of the ratio of the number of occurrences of the digit 7 in the decimal representation of all numbers from 1 to $n$ to the total number of decimal digits in the representation of those same numbers as $n \rightarrow \infty$.

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