
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 ellipse C: $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ with an eccentricity $e= \frac {1}{2}$, and the line $x+y- \sqrt {6}=0$ is tangent to the circle $x^2+y^2=b^2$.
(1) Find the equation of the ellipse;
(2) The line $l$ passing through the point $N(4,0)$ intersects the ellipse at two distinct points $A$ and $B$. The perpendicular bisector of the segment $AB$ is $l'$. Find the range of values for the $y$-intercept $m$ of the line $l'$.

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