
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 ordinary equation of curve $C_1$ is $x^2+y^2-2x=0$. Establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of curve $C_2$ is $\rho^{2}= \frac {3}{1+2\sin^{2}\theta }$.
(I) Find the parametric equation of $C_1$ and the rectangular equation of $C_2$;
(II) The ray $\theta= \frac {\pi}{3}(\rho\geq0)$ intersects $C_1$ at a point $A$ distinct from the pole, and $C_2$ at point $B$. Find $|AB|$.

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