
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
Taking the origin O of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, with both coordinate systems using equal units of length. The parametric equation of line $l$ is given by $$\begin{cases} x=t\sin\phi \\ y=1+t\cos\phi \end{cases}$$ (t is the parameter, $0<\phi<\pi$), and the polar equation of curve $C$ is $\rho\cos^2\theta=4\sin\theta$.

(Ⅰ) Find the general equation of line $l$ and the Cartesian coordinate equation of curve $C$;  
(II) Suppose line $l$ intersects curve $C$ at points A and B, when $\phi$ changes, find the minimum value of $|AB|$.

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