
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 $a_1, a_2, \ldots, a_n$ be a permutation of the numbers 1, 2, \ldots, n. Define the sequence number of $a_i$ (for $i=1,2,\ldots,n$) as the count of numbers that are to the left of $a_i$ and smaller than $a_i$. In the permutations of the numbers 1 to 8, if the sequence number of 8 is 2, the sequence number of 7 is 3, and the sequence number of 5 is 3, determine the number of different permutations.

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