
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 parametric equations of circle $C$ are given by $\begin{cases} x=1+\cos \varphi \\ y=\sin \varphi \end{cases}(\varphi \text{ is the parameter})$. Establish a polar coordinate system with $O$ as the pole and the non-negative half of the $x$-axis as the polar axis.

(I) Find the polar equation of circle $C$;

(II) The ray $OM: \theta = \frac{\pi}{4}$ intersects circle $C$ at points $O$ and $P$. Find the polar coordinates of point $P$.

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