
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 that in the rectangular coordinate system $(xOy)$, the parametric equations of the curve $C\_1$ are $\begin{cases} & x=2\cos \theta \\ & y=\sin \theta \end{cases}$ ($\theta$ is the parameter), and the polar coordinate equation of the curve $C\_2$ is $\rho=2\sin \theta$ with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis.

1. Write out the polar coordinate equation of the curve $C\_1$ and the rectangular coordinate equation of the curve $C\_2$;
2. Given that points $M\_1$ and $M\_2$ have polar coordinates $(1,\dfrac{\mathrm{ }\!\!\pi\!\!{ }}{2})$ and $(2,0)$ respectively, the line $M\_1M\_2$ intersects the curve $C\_2$ at points $P$ and $Q$, and the rays $OP$ and $OQ$ intersect the curve $C\_1$ at points $A$ and $B$ respectively. Calculate the value of $\dfrac{1}{{ }\!|\!{ OA}{{|\!{ }}^{{2}}}}+\dfrac{1}{{ }\!|\!{ OB}{{|\!{ }}^{{2}}}}$.

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