
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 space rectangular coordinate system $O-xyz$, given vectors $\overrightarrow{AB}=(-1,0,1)$, $\overrightarrow{AC}=(0,1,1)$, $\overrightarrow{AD}=(-1,1,0)$.  
$(Ⅰ)$ Find $\overrightarrow{BC}$ and $\overrightarrow{CD}$;  
$(Ⅱ)$ Find a normal vector of the plane $BCD$;  
$(Ⅲ)$ Find the distance from point $A$ to the plane $BCD$.

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