
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
Consider arithmetic sequences \((a_n)\) and \((b_n)\) with all terms integers, starting from \(a_1 = b_1 = 1\) and \(a_2 < b_2\). The sequences satisfy \(a_n + b_n = 2556\) for some \(n\). What is the smallest possible value of \(n\)?
A) 2
B) 3
C) 5
D) 128
E) 637

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