
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
Given a strictly positive integer \( n \), a sequence of \( n \) strictly positive integers is called very nice if it satisfies the following condition: for any positive integer \( k \geq 2 \), if the number \( k \) appears in the sequence, then \( k-1 \) also appears, and moreover, the first appearance of \( k-1 \) occurs before the last appearance of \( k \). How many very nice sequences of length 8 are there?

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