
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 $154,000$ ordered quadruplets \((a, b, c, d)\) such that \(\gcd(a, b, c, d) = 154\) and \(\operatorname{lcm}(a, b, c, d) = n\). What is the smallest possible value for \(n\)?
A) 27340292
B) 51040656
C) 25520328
D) 34680378

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