
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 equation of circle $C$ is given by $\begin{cases} x=1+\cos\phi \\ y=\sin\phi \end{cases}$ ($\phi$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis.

(I) Find the polar equation of circle $C$.
(II) Let $P$ and $Q$ be two moving points on circle $C$ such that $\angle POQ = \frac{\pi}{3}$. Find the maximum value of $|OP| + |OQ|$.

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