
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 $C\_1$: $ρ\sin ^{2}θ=4\cos θ$, with the pole as the coordinate origin and the polar axis as the positive semi-axis, establish the rectangular coordinate system $(xOy)$. The parametric equations of the curve $C\_2$ are $\begin{cases} & x=2+\frac{1}{2}t \\ & y=\frac{\sqrt{3}}{2}t \\ \end{cases}$ (where $t$ is the parameter).

(I) Find the rectangular coordinate equations of $C\_1$ and $C\_2$;

(II) If the curves $C\_1$ and $C\_2$ intersect at points $A$ and $B$, and point $P$ has coordinates $(2,0)$, find the value of $|PA| \cdot |PB|$.

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