
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 $F_{1}$ and $F_{2}$ are the upper and lower foci of the ellipse $\frac{{y}^{2}}{{a}^{2}}+\frac{{x}^{2}}{{b}^{2}}=1(a>b>0)$, a line $l$ passing through point $F_{2}$ with a slope greater than zero intersects the ellipse at points $A$ and $B$. If $|AF_{2}|=2|BF_{2}|$ and $\tan∠AF_{1}B=2\sqrt{2}$, then the eccentricity of the ellipse is ____, and the slope of line $l$ is ____.

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