
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
We know that: if the point $A$ on the number line corresponds to the number $a$, the point $B$ corresponds to the number $b$, and the point $C$ corresponds to the number $c$, the distance between $A$ and $B$ can be represented as $AB=|a-b|$, and the distance between $C$ and $B$ can be represented as $CB=|c-b|$. Given that the number of terms of the polynomial $7x^{3}y^{2}-3x^{2}y-5$ is $a$, the degree is $b$, and the constant term is $c$.  
$(1)$ Write directly: $a=$______, $b=$______, $c=$______; $AC=$______;  
$(2)$ Point $D$ is a point on the number line corresponding to the number $d$.  
① If $BD=6$, find $d$;  
② Write directly the minimum value of the sum of the distances from point $D$ to points $A$, $B$, and $C$ is ______.

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