
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
Consider the ellipse (C) given by the equation $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$. Its left and right foci are $F\_1$ and $F\_2$, respectively, with an eccentricity of $\frac{\sqrt{3}}{2}$. A line passing through $F\_1$ and perpendicular to the x-axis intersects the ellipse (C) in a segment of length $1$.
(I) Find the equation of the ellipse (C);
(II) Suppose point $P$ is any point on ellipse (C) other than the endpoints of the major axis. Connect $PF\_1$ and $PF\_2$, and let the angle bisector of $\angle F\_1PF\_2$ intersect the major axis of (C) at point $M(m, 0)$. Find the range of possible values for $m$.

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