
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: $3x+4x-x=(3+4-1)x=6x$. Similarly, if we consider $(a-b)$ as a whole, then $3(a-b)+4(a-b)-(a-b)=(3+4-1)(a-b)=6(a-b)$. This method of solving problems permeates the "whole idea" in mathematics, which is an important thinking method in solving middle school mathematics problems and has a wide range of applications. Please use the above method to answer the following questions:  
$(1)$ Considering $(a+b)^{2}$ as a whole, then $2(a+b)^{2}-8(a+b)^{2}+3(a+b)^{2}=$______;  
$(2)$ If $x^{2}+2y=4$, find the value of the algebraic expression $-3x^{2}-6y+17$;  
$(3)$ Given $a-3b=3$, $2b-c=-5$, $c-d=9$, find the value of $\left(a-c\right)+\left(2b-d\right)-\left(2b-c\right)$.

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