
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 parametric equation of curve $C_{1}$ is given by
\[
\begin{cases}
x = 1 + \cos \phi \\
y = \sin \phi
\end{cases}
\]
(with $\phi$ as the parameter). By taking the origin $O$ as the pole and the nonnegative half-axis of $x$ as the polar axis, we establish the polar coordinate system, in which the polar equation of curve $C_{2}$ is $\rho = \sin \theta$.

(I) Find the polar equation of curve $C_{1}$ and the Cartesian coordinate equation of curve $C_{2}$.

(II) Given that curves $C_{1}$ and $C_{2}$ intersect at points $O$ and $A$, a line passing through point $O$ and perpendicular to $OA$ intersects curves $C_{1}$ and $C_{2}$ at points $M$ and $N$, respectively. Calculate the length of $|MN|$.

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