
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 a rectangular coordinate system with its origin $O$ as the pole, the positive semi-axis of the $x$-axis as the polar axis, and both coordinate systems having equal length units, the parameteric equation of line $l$ is $\begin{cases} x=t \sin \theta \\ y=2+t \cos \theta \end{cases}$ ($t$ is the parameter, $0 < \theta < \pi$), and the polar coordinate equation of curve $C$ is $\rho \cos^2 \theta = 8 \sin \theta$.

(1) Find the general equation of line $l$ and the rectangular coordinate equation of curve $C$.

(2) Suppose line $l$ intersects curve $C$ at points $A$ and $B$. As $\theta$ varies, find the minimum value of $|AB|$.

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