
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 $$\begin{cases} x=cos\phi \\ y=1+sin\phi \end{cases}$$ (where $\phi$ is the parameter). Establish a polar coordinate system with O as the pole and the non-negative x-axis as the polar axis.
(I) Find the polar equation of circle C;
(II) The ray $OM: \theta = \frac{\pi}{3}$ intersects circle C at points O and P, and intersects curve $C_1: y = \frac{3\sqrt{3}}{x}$ (x>0) at point Q. Find the length of line segment PQ.

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