
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
The vectors of the normal planes $\alpha$ and $\beta$ are perpendicular if and only if their dot product is equal to 0. Given that the normal vector of plane $\alpha$ is $\left(3,1,-2\right)$ and the normal vector of plane $\beta$ is $\left(-1,1,k\right)$, find the value of $k$.

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