
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
The center of an ellipse is at the origin $O$, its minor axis length is $2 \sqrt{2}$, and the directrix $l$ corresponding to the focus $F(c, 0)(c>0)$ intersects the $x$-axis at point $A$. Given that $|O F|=2|F A|$, a line passing through point $A$ intersects the ellipse at points $P$ and $Q$.
(1) Find the equation of the ellipse and its eccentricity.
(2) If $\overrightarrow{O P} \cdot \overrightarrow{O Q}=0$, find the equation of the line $P Q$.

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