
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
Given the parametric equation of curve $C_{1}$: 
$$
\left\{ 
\begin{array}{l}
x = 1 + \cos \theta \\
y = 1 + \sin \theta
\end{array}
\right.
(\theta \text{ is the parameter}),
$$
establishing a polar coordinate system with the origin as the pole and positive $x$-axis as the polar axis, the polar equation of curve $C_{2}$ is $\rho=1$.

(I) Convert the parametric equation of $C_{1}$ into a Cartesian equation, and the polar equation of $C_{2}$ into a Cartesian equation;

(II) Find the polar coordinates $(\rho,\theta) (\rho \geqslant 0, 0 \leqslant \theta < 2\pi)$ of the intersection points of $C_{1}$ and $C_{2}$.

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