
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
Let \( a_{n} \) denote the number of \( n \)-digit decimal numbers in the interval \([0,1)\) that do not contain the digit 9, and let \( S_{n} \) denote the sum of these numbers. Then,
$$
\lim _{n \rightarrow \infty} \frac{S_{n}}{a_{n}}=
$$

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