
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
For each positive integer \( n \), let
\[
a_n = \frac{(n+7)!}{(n-1)!}
\]
Let \( k \) denote the smallest positive integer for which the rightmost nonzero digit of \( a_k \) is 1. What is the rightmost nonzero digit of \( a_k \)?
A) 1
B) 3
C) 5
D) 7
E) 9

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