
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 equations of curve $C\_1$ as $\begin{cases} & x=2-t \\\\ & y=\sqrt{3}t \end{cases}$ ($t$ is the parameter), when $t=-1$, the corresponding point on the curve $C\_1$ is $A$, and the point symmetric to $A$ with respect to the origin is $B$. Establish a coordinate system with the origin $O$ as the pole and the $x$-axis as the positive polar axis. The polar equation of curve $C\_2$ is $\rho = \dfrac{6}{\sqrt{9-3\sin^{2}\theta}}$.

(1) Find the polar coordinates of points $A$ and $B$.
(2) Let $P$ be a moving point on curve $C\_2$, find the maximum value of $|PA|^2 + |PB|^2$.

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