
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
In the Cartesian coordinate system $(xOy)$, the parametric equations of line $l$ are given by $\begin{cases} x = -2 + \frac{1}{2}t \\ y = 2 + \frac{\sqrt{3}}{2}t \end{cases}$ ($t$ is the parameter). A polar coordinate system is established with $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of curve $C$ is $\rho^2 \cos 2\theta + 4\rho \sin \theta - 3 = 0$.

(1) Convert the polar equation of curve $C$ to a rectangular equation.
(2) If line $l$ intersects curve $C$ at points $A$ and $B$, find the length of $|AB|$.

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