
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
The ellipse $C$: $\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$ ($a > b > 0$) has its center at the origin, its foci on the x-axis, a focal distance of 2, and shares the same eccentricity with the ellipse $x^{2} + \frac {y^{2}}{2} = 1$. The line $l: y = kx + m$ intersects ellipse $C$ at two distinct points $A$ and $B$.  
(I) Find the equation of ellipse $C$;  
(II) If there exists a point $Q$ on ellipse $C$ such that $\overrightarrow {OA} + \overrightarrow {OB} = \lambda \overrightarrow {OQ}$, (where $O$ is the coordinate origin), find the range of values for the real number $\lambda$.

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