
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 $110,000$ ordered quadruplets $(a, b, c, d)$ such that $\gcd(a, b, c, d) = 110$ and $\operatorname{lcm}(a, b, c, d) = n$. What is the smallest possible value for $n$?
A) 150800
B) 180900
C) 198000
D) 221000
E) 245000

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