
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 $\begin{cases} x=3\cos \phi \ y=3+3\sin \phi \end{cases} (\phi \text{ is the parameter})$. Establish a polar coordinate system with $O$ as the pole and the non-negative semi-axis of the $x$-axis as the polar axis.

(1) Find the general equation of circle $C$;
(2) The polar equation of line $l$ is $2\rho \sin \left( \theta - \frac{\pi }{6} \right) = 4\sqrt{3}$, and the intersection point of ray $OM: \theta = \frac{5\pi }{6}$ with circle $C$ is $P$, and with line $l$ is $Q$. Find the length of line segment $PQ$.

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