
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
There are exactly $90,000$ ordered quadruplets $(a, b, c, d)$ such that $\gcd(a, b, c, d) = 90$ and $\operatorname{lcm}(a, b, c, d) = n$. What is the smallest possible value for $n$?
A) 32,400
B) 36,000
C) 40,500
D) 45,000

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