
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 $(C)$: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$, with an eccentricity of $\frac{\sqrt{3}}{2}$, and two foci $F\_1$, $F\_2$. A line passing through $F\_1$ intersects the ellipse $(C)$ at points $M$ and $N$, and the perimeter of $\triangle F\_2MN$ is $8$.

(1) Find the equation of the ellipse $(C)$;

(2) A line $(l)$ tangent to the circle $x^{2}+y^{2}=1$ passes through point $P(m,0)$ and intersects the ellipse $(C)$ at points $A$ and $B$. Find the maximum value of the chord length $|AB|$.

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