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

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