
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
Given two arithmetic sequences \((a_n)\) and \((b_n)\) where each sequence starts from 1 and the terms are integers, where \( a_1 = b_1 = 1\) and \(a_2 \leq b_2\). Let\((a_n \times b_n= 4021)\) for some n. Find the largest possible value of \(n\).
A) 10
B) 11
C) 12
D) 66
E) 67

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