
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 Cartesian coordinate system $xOy$, the curve $$C_{1}: (x-1)^{2}+y^{2}=1$$, and the parametric equation of curve $C_{2}$ is: $$\begin{cases} x= \sqrt {2}\cos\theta \\ y=\sin\theta\end{cases}$$, (where $\theta$ is the parameter), with $O$ as the pole and the positive half-axis of $x$ as the polar axis in the polar coordinate system.  
(1) Find the polar equations of $C_{1}$ and $C_{2}$.  
(2) The ray $$y= \frac { \sqrt {3}}{3}x(x\geq0)$$ intersects with $C_{1}$ at a point $A$ different from the origin, and intersects with $C_{2}$ at point $B$. Find $|AB|$.

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