
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 each positive integer $n$ denote the following sequence:
\[ b_n = \frac{(n+14)!}{(n-1)!} \]
Find the smallest positive integer $k$ for which the rightmost nonzero digit of $b_k$ is an even number.
A) 2
B) 4
C) 6
D) 8
E) 0

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