
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 with the circle $x^2 + y^2 = 4$ at two distinct points A and B, where O is the origin, and the following inequality holds: $\left| \overrightarrow{OA} + \overrightarrow{OB} \right| \geq \frac{\sqrt{3}}{3} \left| \overrightarrow{AB} \right|$, find the range of values for k.

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