
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 \((b_n)\) have integer terms with \(a_1 = b_1 = 1 < a_2 \le b_2\) and \(a_n b_n = 1540\) for some \(n\). What is the largest possible value of \(n\)?
A) 3   
B) 21  
C) 73  
D) 219  
E) 512

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