
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 on the number line, points $A$ and $B$ represent the numbers $a$ and $b$ respectively, and $a$ and $b$ satisfy $|a+12|+(b-20)^{2}=0$.  
$(1)$ Write down the values of $a$ and $b$ directly.  
$(2)$ If point $C$ represents the number $4$, points $M$ and $N$ start moving towards each other at constant speeds from points $A$ and $B$ respectively. The speed of point $M$ is $5$ units per second, and the speed of point $N$ is $3$ units per second. Let $t$ be the time in seconds for the motion of the two points:  
① When point $M$ is between $A$ and $C$, and $CM=BN$, find the value of $t$ at this time.  
② When point $N$ reaches point $A$, it immediately returns at the original speed, stops after reaching point $C$; when point $M$ reaches point $B$, it immediately returns at the original speed, returns to point $A again at the same speed, and continues to move back and forth between $A$ and $B$ until point $N$ stops moving. Find the value of $t$ when points $M$ and $N$ meet during this motion.

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