
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 $$\begin{cases} x=1+\cos\alpha \\ y=\sin\alpha \end{cases}$$ (where α is the parameter), and the curve C₂ is $$\frac{x^{2}}{3}+y^{2}=1$$．
(1) In the polar coordinate system with O as the pole and the positive semi-axis of the x-axis as the polar axis, find the polar equations of C₁ and C₂;
(2) The ray $$\theta= \frac {\pi}{3}(\rho \geq 0)$$ intersects with C₁ at point A (A is not the pole), and with C₂ at point B, find |AB|.

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