
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 polar coordinate system with origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, and the same unit length for both coordinate systems. A line $l$ is defined by the parametric equations $\begin{cases} x=t\cos\varphi \\ y=2+t\sin\varphi \end{cases}$ (where $t$ is a parameter, $0\leqslant \varphi < \pi$), and a curve $C$ is given by the polar equation $\rho\cos^2\theta = 8\sin\theta$.

(1) Find the standard 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 $\varphi$ varies, find the minimum value of $|AB|$.

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