
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
Define \( n_a! \) for \( n \) and \( a \) positive to be 
\[
n_a ! = n (n-a)(n-2a)(n-3a)\ldots (n-ka)
\]
where \( k \) is the greatest integer for which \( n > ka \). Calculate the quotient \( 90_9!/30_3!/3 \).
A) \(3^9\)  
B) \(6^9\)  
C) \(9^9\)  
D) \(9^{12}\)

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