
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: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a > b > 0)$$ passes through the point $(1, \frac{2\sqrt{3}}{3})$. The foci are denoted as F<sub>1</sub> and F<sub>2</sub>. The chord length formed by the intersection of the circle $x^2 + y^2 = 2$ and the line $x + y + b = 0$ is equal to 2.

(Ⅰ) Find the standard equation of ellipse C;
(Ⅱ) Let Q be a point on ellipse C that is not on the x-axis, denoted as Q(x<sub>0</sub>, y<sub>0</sub>). Taking O as the coordinate origin, draw a line through F<sub>2</sub> parallel to OQ, intersecting the ellipse C at two distinct points M and N. Find the range of values for $$\frac{|MN|}{|OQ|}$$.

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