
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 $\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1 (a > b > 0)$ with vertex $B$ at the top, vertex $A$ on the right, and right focus $F$. Let $E$ be a point on the lower half of the ellipse such that the tangent at $E$ is parallel to $AB$. If the eccentricity of the ellipse is $\frac {\sqrt{2}}{2}$, then the slope of line $EF$ is __________.

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