
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
Suppose 4-4: Coordinate System and Parametric Equations

In the rectangular coordinate system $xOy$, the parametric equation of the line $l$ is $\begin{cases} & x=\sqrt{3}+t\cos \frac{\pi }{4}, \\ & y=t\sin \frac{\pi }{4} \end{cases}\ (t\text{ is the parameter})$, and the polar coordinate system is established with the origin as the pole and the ray $Ox$ as the polar axis. The polar equation of the curve $C$ is $\frac{\rho^2 \cos^2 \theta}{4}+\rho^2 \sin^2 \theta =1$.

(1) Find the rectangular coordinate equation of the curve $C$.

(2) Find the length of the chord $AB$ obtained by the intersection of the line $l$ and the curve $C$.

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