
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 vector $\overrightarrow{b}$ is collinear with vector $\overrightarrow{a}=(2,-1,2)$, and satisfies $\overrightarrow{a} \cdot \overrightarrow{b}=18$, $(k \overrightarrow{a}+ \overrightarrow{b}) \perp (k \overrightarrow{a}- \overrightarrow{b})$, find the value of vector $\overrightarrow{b}$ and $k$.

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