
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 points $F\_1$ and $F\_2$ are the left and right foci of the ellipse $C$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, respectively, and $P$ is a point on the ellipse $C$ with $|F\_1F\_2|=2$, $\angle F\_1PF\_2 = \frac{\pi}{3}$, and the area of $\triangle F\_1PF\_2$ is $\frac{\sqrt{3}}{3}$.
(I) Find the equation of the ellipse $C$;
(II) The coordinates of point $M$ are $(\frac{5}{4}, 0)$, and the line $l$ passing through point $F\_2$ with slope $k$ intersects the ellipse $C$ at points $A$ and $B$. Is $\overrightarrow{MA} \cdot \overrightarrow{MB}$ a constant value for any $k \in \mathbb{R}$? If so, find this constant value; if not, explain the reason.

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