
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 $\left(a_n\right)$ and $\left(b_n\right)$ have integer terms with $a_1=2, b_1=3$ and $3a_2 < 2b_2$. If $a_n b_n = 4032$ for some $n$, what is the largest possible value of $n$?
A) 2
B) 11
C) 61
D) 367
E) 4026

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