
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 three-dimensional Cartesian coordinate system, given points $A(2,a,-1)$, $B(-2,3,b)$, $C(1,2,-2)$.<br/>$(1)$ If points $A$, $B$, and $C$ are collinear, find the values of $a$ and $b$;<br/>$(2)$ Given $b=-3$, $D(-1,3,-3)$, and points $A$, $B$, $C$, and $D$ are coplanar, find the value of $a$.

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