
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 that the points $A$ and $B$ on the number line correspond to the numbers $a$ and $b$, respectively, and satisfy $|a+20|+|b-12|=0$. Points $A$ and $B$ start moving at a constant speed along the number line simultaneously, with point $A$ moving at a speed of $6$ units per second and point $B$ moving at a speed of $2$ units per second. The duration of the motion is $t$ seconds.  
$(1)$ Write down the values of $a=$______ and $b=$______.  
$(2)$ If points $A$ and $B$ start moving towards each other at a constant speed, and at time $t$ point $A$ is at the same distance from the origin as point $B$, find the value of $t$.  
$(3)$ During the motion of points $A$ and $B$, if at time $t$ they are $8$ units apart, find the value of $t$.

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