
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 that the foci of an ellipse are $F_{1}(-1,0)$ and $F_{2}(1,0)$, and the ellipse shares a common point with the line $x-y+3=0$, find the equation of the ellipse with the maximum eccentricity.
A) $ \dfrac {x^{2}}{20}+ \dfrac {y^{2}}{19}=1$
B) $ \dfrac {x^{2}}{9}+ \dfrac {y^{2}}{8}=1$
C) $ \dfrac {x^{2}}{5}+ \dfrac {y^{2}}{4}=1$
D) $ \dfrac {x^{2}}{3}+ \dfrac {y^{2}}{2}=1$

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