
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 rectangular coordinate system xOy, the parametric equations of the curve C₁ are $$\begin{cases} x=1+\cos\theta \\ y=\sin\theta \end{cases}$$ (where θ is the parameter), and the curve C₂ has the polar coordinate equation ρ=4sinθ, with the coordinate origin O as the pole and the positive semi-axis of x as the polar axis.
(1) Find the polar coordinate equation of curve C₁ and the rectangular coordinate equation of curve C₂.
(2) Curves C₁ and C₂ intersect at points A and B. Find the length of line segment AB.

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