
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 $(xOy)$, curve $C_{1}$ is defined by the equation $(x-1)^{2}+y^{2}=1$, and curve $C_{2}$ is defined by the parametric equations $\begin{cases} x = \sqrt{2}\cos \theta \\ y = \sin \theta \end{cases}$ where $\theta$ is the parameter. Establish a polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis.

(1) Find the polar equations of $C_{1}$ and $C_{2}$;
(2) The ray $y=\frac{\sqrt{3}}{3}x (x \geqslant 0)$ intersects with $C_{1}$ at point $A$ (excluding the origin) and intersects with $C_{2}$ at point $B$. Find the distance $|AB|$.

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