
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 $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ that passes through the point $(1, \frac{2 \sqrt{3}}{3})$, with left and right foci $F\_1$, $F\_2$, respectively. The circle $x^{2}+y^{2}=2$ intersects the line $x+y+b=0$ with a chord length of $2$.

(I) Find the standard equation of the ellipse $C$.
(II) Let $Q$ be a moving point on the ellipse $C$ not located on the $x$-axis. Draw a line parallel to $OQ$ (where $O$ is the origin) through the focus $F\_2$ 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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