
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 that $a$ is a real constant, the parametric equation of curve C₁ is $$\begin{cases} x=2t^{2}-4t \\ y=4t-4 \end{cases}$$ (where $t$ is the parameter), and curve C₂'s polar coordinate equation is cosθ=$a$sinθ in a polar coordinate system established with origin O as the pole and positive semi-axis of the x-axis as the polar axis.
(1) Write the Cartesian equation of C₁ and the Cartesian equation of C₂.
(2) Suppose curves C₁ and C₂ intersect at points A and B. Find the minimum value of |AB|.

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