
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 the parametric equations of curve $C\_1$ are $ \begin{cases} x=2\cos φ \\\\ y=3\sin φ\end{cases} (φ \text{ is the parameter})$, a coordinate system is established with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The polar coordinate equation of curve $C\_2$ is $ρ=2$. The vertices of square $ABCD$ are all on $C\_2$, and points $A$, $B$, $C$, $D$ are arranged in counterclockwise order. The polar coordinates of point $A$ are $(2, \dfrac {π}{2})$.

1. Find the rectangular coordinates of points $A$, $B$, $C$, $D$;
2. Suppose $P$ is any point on $C\_1$, find the range of values for $|PA|^{2}+|PB|^{2}+|PC|^{2}+|PD|^{2}$.

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