
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 the parabola $C$: $y=2x^{2}$ and the line $y=kx+2$ intersect at points $A$ and $B$. $M$ is the midpoint of segment $AB$. A vertical line is drawn through $M$ intersecting the $x$-axis at point $N$. If $\overrightarrow{NA} \cdot \overrightarrow{NB}=0$, then $k=$ \_\_\_\_\_\_.

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