
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
Determine \(k\) such that the polynomial \(4x^3 - 8x^2 + kx - 16\) is divisible by \(x - 2\). Then, identify which of the given options is also a factor of the polynomial.
A) \( x^2 + 4 \)  
B) \( 4x^2 + 4 \)  
C) \( x^2 - 1 \)  
D) \( x^2 + 1 \)

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