
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
Let the ellipse $$\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a＞b＞0)$$ have its left focus at F, its top vertex at A, and a line through point A perpendicular to AF intersects the ellipse and the positive x-axis at points P and Q, respectively, with AP:PQ = 8:5.  
(1) Find the eccentricity of the ellipse;  
(2) Given that line l passes through point M(-3,0) with an angle of inclination $$\frac {π}{6}$$, and circle C passes through points A, Q, F, if line l is tangent to circle C, find the equation of the ellipse.

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