
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
In the Cartesian coordinate system xOy, let the ellipse C1: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a > b > 0)$$ have its left and right foci at F1 and F2, respectively. F2 is also the focus of the parabola C2: $y^2 = 4x$. Let point M be the intersection of C1 and C2 in the first quadrant, and let $|MF_2| = \frac{5}{3}$.
(Ⅰ) Find the equation of C1;
(Ⅱ) Suppose point N on the plane satisfies $\overrightarrow{MN} = \overrightarrow{MF_1} + \overrightarrow{MF_2}$. Let line l be parallel to MN and intersect C1 at points A and B. If $\overrightarrow{OA} \cdot \overrightarrow{OB} = 0$, find the equation of line l.

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