
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
Given the Cartesian coordinate system, the parametric equations of curve $C\_1$ are $x=\sqrt{3}+3\cos φ$, $y=-1+3\sin φ$ where $φ$ is the parameter. Establish a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis. The polar equation of curve $C\_2$ is $ρ=2\cos θ$.
(I) Find the polar equation of curve $C\_1$ and the Cartesian equation of curve $C\_2$;
(II) If line $θ=\frac{π}{6}$ ($ρ∈\mathbb{R}$) intersects curve $C\_1$ at points $P$ and $Q$, find the length of $\vert PQ \vert$.

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