
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's define $n_a!$ where $n$ and $a$ are positive integers as \[n_a! = n(n-a)(n-2a)...(n-ka)\], where $k$ is the highest integer such that $n > ka$. Find the value of $\frac{36_6!}{12_3!}$.
A) 51840
B) 103680
C) 207360
D) 311040

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