
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 circle C is $$\begin{cases} \overset{x=1+\cos\theta }{y=\sin\theta }\end{cases}$$ (where $\theta$ is the parameter). A polar coordinate system is established with O as the pole, the non-negative half-axis of x as the polar axis, and the same unit length is taken.

(1) Find the polar equation of circle C;  
(2) If the polar equation of line $l$ is $$2\rho\sin(\theta+ \frac {\pi}{3})=3 \sqrt {3}$$, and the ray $$OM: \theta= \frac {\pi}{3}$$ intersects circle C at points O and P, and intersects line $l$ at point Q. Find the length of segment PQ.

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