
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
When \( (a-b)^n, n\ge2, a\ne b, ab\ne0 \) is expanded by the binomial theorem, it is discovered that if \( a=kb+c \) where \( k \) is a positive integer and \( c \neq 0, c \neq b(k-1) \), the sum of the first two terms of the expansion is zero. Find the value of \( n \).
A) 2b  
B) -2b  
C) \(\frac{-b(k-1)}{c}\)  
D) k+1

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