
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 parametric equation of curve $C\_1$ as $\begin{cases} x=a\cos \theta \\ y=b\sin \theta \end{cases}$ $(a > b > 0, \theta$ is the parameter$)$, and the point $M(1, \frac{ \sqrt{3}}{2})$ on curve $C\_1$ corresponds to the parameter $\theta= \frac{ \pi}{3}$. Establish a polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar coordinate equation of curve $C\_2$ is $ρ=2\sin θ$.

1. Write the polar coordinate equation of curve $C\_1$ and the rectangular coordinate equation of curve $C\_2$;
2. Given points $M\_1$ and $M\_2$ with polar coordinates $(1, \frac{ \pi}{2})$ and $(2,0)$, respectively. The line $M\_1M\_2$ intersects curve $C\_2$ at points $P$ and $Q$. The ray $OP$ intersects curve $C\_1$ at point $A$, and the ray $OQ$ intersects curve $C\_1$ at point $B$. Find the value of $\frac{1}{|OA|^{2}}+ \frac{1}{|OB|^{2}}$.

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