
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 $$\begin{cases} x=2-t \\ y= \sqrt {3}t \end{cases}$$ (where $t$ 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 coordinate system with the origin O as the pole and the x-axis as the positive semi-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}
user