
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 $$\begin{cases} x=2-t \\ y= \sqrt {3}t \end{cases}, (t\text{ is the parameter})$$, when $t=-1$, it corresponds to a point $A$ on curve $C_1$, and the symmetric point of $A$ with respect to the origin is $B$. Establishing a polar coordinate system with the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_2$ is $$\rho= \frac {6}{ \sqrt {9+3\sin^{2}\theta}}$$.
(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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