
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 process of solving mathematical problems, we often use the mathematical concept of "classification discussion." Below is the process of solving problems using the concept of classification discussion. Please read carefully and answer the question.  
【Problem】Three rational numbers $a$, $b$, $c$ satisfy $abc > 0$. Find the value of $\frac{|a|}{a}+\frac{|b|}{b}+\frac{|c|}{c}$;  
【Solution】Solution: According to the problem, the three rational numbers $a$, $b$, $c$ are all positive numbers or one of them is positive and the other two are negative.  
① If $a$, $b$, $c$ are all positive, i.e., $a > 0$, $b > 0$, $c > 0$, then $\frac{|a|}{a}+\frac{|b|}{b}+\frac{|c|}{c}=\frac{a}{a}+\frac{b}{b}+\frac{c}{c}=1+1+1=3$;  
② If one of $a$, $b$, $c$ is positive and the other two are negative, assume $a > 0$, $b < 0$, $c < 0$, then $\frac{|a|}{a}+\frac{|b|}{b}+\frac{|c|}{c}=\frac{a}{a}+\frac{-b}{b}+\frac{-c}{c}=1+(-1)+(-1)=-1$;  
Therefore, the value of $\frac{|a|}{a}+\frac{|b|}{b}+\frac{|c|}{c}$ is $3$ or $-1$.  
【Exploration and Extension】Based on the above solution, answer the following questions:  
$(1)$ Given that $a$, $b$ are non-zero rational numbers, when $|ab|=-ab$, the value of $\frac{a}{|a|}+\frac{b}{|b|}$ is ______;  
$(2)$ Given that $a$, $b$, $c$ are rational numbers, when $abc < 0$, find the value of $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}$;  
$(3)$ If $abc \neq 0$ and $a+b+c=0$, then the value of $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|}$ is.

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