
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 xy-plane of the rectangular coordinate system, establish a polar coordinate system with the origin O as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of the curve C is given by ρ(1 + cos2θ) = 8sinθ.
(1) Find the Cartesian equation of the curve C.
(2) The parametric equations of the line l are given by $$\begin{cases} x=t\cos\alpha, \\ y=1+t\sin\alpha \end{cases}$$ (where t is the parameter). The line l intersects the y-axis at point F and intersects the curve C at points A and B. When |FA|•|FB| is at its minimum, find the Cartesian equation of the line l.

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