
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 left focus of the ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$ be $F$, the top vertex be $A$, and a ray of light passing through point $A$ and perpendicular to $AF$ reflects off the ellipse's right directrix. The reflected ray is parallel to line $AF$.  
(1) Find the eccentricity of the ellipse;  
(2) Let the intersection of the incident ray and the right directrix be $B$. The circle passing through points $A$, $B$, $F$ is tangent to the line $3x-y+3=0$. Find the equation of the ellipse.

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