
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 an eccentricity of $\frac{\sqrt{3}}{3}$, and a line $l$: $y=x+2$ that is tangent to a circle $O$ with the center at the origin and a radius equal to the length of the minor axis of the ellipse $C$.

(1) Find the equation of the ellipse $C$;

(2) A line $m$ passes through the left vertex $A$ of the ellipse $C$ and intersects the circle $O$ at two points $R$ and $S$, forming an obtuse triangle $ORS$. Find the range of the slope $k$ of the line $m$.

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