
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 that $F\_1$ and $F\_2$ are the left and right foci, respectively, of an ellipse $E$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$ with an eccentricity of $\frac{1}{2}$. $M$ is a point on the ellipse $E$, and the midpoint of the line segment $F\_1M$ is $N$. The perimeter of $\triangle NF\_1O$ (where $O$ is the coordinate origin) is 3.

(I) Find the standard equation of the ellipse $E$;

(II) A line $l$, not perpendicular to the $x$-axis, is drawn through $F\_1$, intersecting the ellipse $E$ at points $A$ and $B$. $Q(m, 0)$ is a point on the $x$-axis such that $|QA| = |QB|$. Find the range of values for the real number $m$.

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