
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 $n$, define the sequence $b_n = \frac{(2n + 8)!}{n!}$. Let $m$ denote the smallest positive even integer for which the rightmost nonzero digit of $b_m$ is even. Find the rightmost nonzero digit of $b_m$.
A) 2  
B) 4  
C) 6  
D) 8  
E) 0

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