
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
Arithmetic sequences \((a_n)\) and \((b_n)\) consist of integer terms with initial values \(a_1 = b_1 = 1\), and common differences \(x\) and \(y\), respectively. It is known that \(1 < a_2 \leq b_2\) and \(a_n \cdot b_n = 1764\) for some \(n\). Determine the largest possible value of \(n\).
A) 8
B) 41
C) 42
D) 44
E) 1764

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