
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 curve $C\_1$: $\begin{cases} & x=1+\dfrac{\sqrt{2}}{2}t \\ & y=\dfrac{\sqrt{2}}{2}t \\ \end{cases}$ ($t$ is a parameter), establish a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis. The curve $C\_2$: $\dfrac{1}{\rho^{2}}=\dfrac{\cos^{2}\theta}{2}+\sin^{2}\theta$.

(I) Write the general equation of the curve $C\_1$ and the rectangular coordinate equation of the curve $C\_2$;

(II) If $M(1,0)$, and the curve $C\_1$ intersects with the curve $C\_2$ at two distinct points $A$ and $B$, find the value of $\dfrac{|MA|\cdot |MB|}{|AB|}$.

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