
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 that $\overrightarrow{a}$ and $\overrightarrow{b}$ are non-zero and non-collinear vectors, the vector $8\overrightarrow{a}-k\overrightarrow{b}$ is collinear with $-k\overrightarrow{a}+\overrightarrow{b}$. Find the value of $k$.
A) $2\sqrt{2}$
B) $-2\sqrt{2}$
C) $\pm 2\sqrt{2}$
D) $8$

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