
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
Let $F$ be the focus of the parabola $C$: $y^{2}=2x$, and $A$, $B$ are two moving points on the parabola $C$.  
(Ⅰ) If the line $AB$ passes through the focus $F$ and has a slope of $2$, find $|AB|$;  
(Ⅱ) If the line $l$: $x-y+4=0$, find the minimum distance from point $A$ to the line $l$.

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