
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 selected topic 4-4 on coordinate systems and parametric equations, the parametric equation of curve $C_1$ is given by 
$$
\begin{cases}
x = 2\cos\phi \\
y = 3\sin\phi
\end{cases}
(\text{where } \phi \text{ is the parameter}).
$$
Using the origin as the pole and the positive x-axis as the polar axis, the equation for curve $C_2$ in this coordinate system is $\rho = 2$. The vertices of the square $ABCD$ are on $C_2$, and the vertices $A$, $B$, $C$, and $D$ are arranged in counterclockwise order. The polar coordinates of point $A$ are $(2, \frac{\pi}{3})$.  
(1) Find the Cartesian coordinates of points $A$, $B$, $C$, and $D$.  
(2) Let $P$ be any point on $C_1$. Determine 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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