
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 three points in space $A(-2,0,2)$, $B(t-2,4,3)$, $C(-4,s,1)$, let $\overrightarrow{a}=\overrightarrow{AB}$, $\overrightarrow{b}=\overrightarrow{AC}$.  
$(1)$ If $t=2$, when points $A$, $B$, $C$ are collinear, find the value of $s$.  
$(2)$ If $s=2$, and $\overrightarrow{a}+\overrightarrow{b}$ is perpendicular to $\overrightarrow{b}$, find the value of $t$.

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