
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 points $A$, $B$, $C$ with coordinates $(0,1,2)$, $(1,2,3)$, $(1,3,1)$ respectively.  
$(1)$ If $\overrightarrow{AD}=(3,y,1)$ and $\overrightarrow{AD}\perp \overrightarrow{AC}$, find the value of $y$;  
$(2)$ If the coordinates of point $D$ are $(x,5,3)$ and points $A$, $B$, $C$, $D$ are coplanar, find the value of $x$.

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