
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 $e = \frac {1}{2}$, and the length of the major axis is 4,
(Ⅰ) Find the equation of ellipse C;
(Ⅱ) $F_1$ and $F_2$ are the two foci of ellipse C, and ⊙O is the circle with diameter $F_1F_2$. A line $l: y = kx + m$ is tangent to ⊙O and intersects ellipse C at two distinct points A and B. If $\vec {OA} \cdot \vec {OB} = -\frac {3}{2}$, find the value of $k$.

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