
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 three points in space A(-2, 0, 2), B(-1, 1, 2), and C(-3, 0, 4), let $\overrightarrow{a} = \overrightarrow{AB}$, $\overrightarrow{b} = \overrightarrow{AC}$. If the vector $k\overrightarrow{a} + \overrightarrow{b}$ is perpendicular to $k\overrightarrow{a} - 2\overrightarrow{b}$, then the value of $k$ is ______.

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