
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 line $x+y-k=0$ ($k > 0$) intersects the circle $x^{2}+y^{2}=4$ at two distinct points $A$ and $B$, and $O$ is the origin. Find the range of $k$ such that $| \overrightarrow{OA}+ \overrightarrow{OB}|\geqslant \dfrac { \sqrt {3}}{3}| \overrightarrow{AB}|$.

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