
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
We say that an integer \( m \) covers the number 1998 if \( 1, 9, 9, 8 \) appear in this order as digits of \( m \). For instance, 1998 is covered by 215993698 but not by 213326798. Let \( k(n) \) be the number of positive integers that cover 1998 and have exactly \( n \) digits (\( n \geq 5 \)), all different from 0. What is the remainder of \( k(n) \) in division by 8?

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