
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, with O being the origin, and it is given that $$|\vec{OA} + \vec{OB}| \geq \frac{\sqrt{3}}{3}|\vec{AB}|$$, determine the range of values for $k$.

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