
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
In a positive integer in the decimal system, if it contains an even number (including zero) of the digit 8, it is called a "good number"; otherwise, it is called a "non-good number." How many "good numbers" are there with a length (number of digits) not exceeding \( n \) (where \( n \) is a positive integer)?

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