
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
An ellipse (C) is given by the equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (where $a > b > 0$). Its center is at the origin, the foci lie on the x-axis, the focal length is 2, and it shares the same eccentricity with the ellipse $x^2 + \frac{y^2}{2} = 1$. A line (l) defined by $y = kx + m$ intersects the ellipse (C) at two distinct points A and B.

(I) Find the equation of the ellipse (C);
(II) If there exists a point Q on the ellipse (C) that satisfies $\overrightarrow{OA} + \overrightarrow{OB} = \lambda \overrightarrow{OQ}$ (where O is the coordinate origin), find the range of real number values for $\lambda$.

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