
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 point O at the origin of a rectangular coordinate system and the positive semi-axis of the x-axis as the polar axis, with both coordinate systems having equal length units, the parametric equation of line l is given by $ \begin{cases} x=t\cos \alpha \\ y=2+t\sin \alpha \end{cases} (t \text{ is the parameter, } 0\leqslant \alpha < \pi) $, and the polar coordinate equation of curve C is $ \rho\cos ^{2}\theta=4\sin \theta $.
(1) If $ \alpha= \dfrac {\pi}{6} $, 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. Find the minimum value of |AB| as $ \alpha $ varies.

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