
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 polar coordinate system, the curve $C\_1$: $ρ=2\cos θ$, and the curve $C\_2$: $ρ\sin ^{2}θ=4\cos θ$. Establish a rectangular coordinate system $(xOy)$ with the pole as the coordinate origin and the polar axis as the positive semi-axis $x$. The parametric equation of the curve $C$ is $\begin{cases} x=2+ \frac {1}{2}t \ y= \frac {\sqrt {3}}{2}t\end{cases}$ ($t$ is the parameter).
(I) Find the rectangular coordinate equations of $C\_1$ and $C\_2$;
(II) The curve $C$ intersects $C\_1$ and $C\_2$ at four distinct points, arranged in order along $C$ as $P$, $Q$, $R$, and $S$. Find the value of $||PQ|-|RS||$.

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