
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
In the Cartesian coordinate system $xOy$, the parabola $y^{2}=2px(p > 0)$ has its focus at $F$, and its directrix intersects the $x$ axis at point $H$. A line $l$ passing through $H$ intersects the parabola at points $A$ and $B$, and $|BF|=2|AF|$.  
(Ⅰ) Find the slope of line $AB$;  
(Ⅱ) If the area of $\triangle ABF$ is $\sqrt{2}$, find the equation of the parabola.

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