
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 an ellipse $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ with eccentricity $\frac{\sqrt{3}}{3}$, and a line $l$: $y = x + 2$ is tangent to a circle $O$ centered at the origin with the minor axis of ellipse $C$ as its radius.  
$(1)$ Find the equation of ellipse $C$;  
$(2)$ Through the left vertex $A$ of ellipse $C$, draw line $m$ intersecting circle $O$ at two points $R$, $S$. If $\triangle ORS$ is an obtuse triangle, find the range of values for the slope $k$ of line $m$.

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