
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 an ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$ where $a>b>0$, which passes through the point $(-3, 2)$ and has an eccentricity of $\frac {\sqrt {3}}{3}$. The circle, ⊙O, has its center at the origin with its diameter equal to the short axis of the ellipse. The equation of circle ⊙M is $(x-8)^{2}+(y-6)^{2}=4$. For any point P on ⊙M, tangent lines PA and PB are drawn to ⊙O with tangent points A and B respectively.  
(1) Find the equation of the ellipse;  
(2) If line PA intersects ⊙M again at point Q, when chord PQ is at its maximum length, find the equation of line PA;  
(3) Find the maximum and minimum values of $\overrightarrow {OA}\cdot \overrightarrow {OB}$.

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