
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
【Reading Material】We know that $4x-2x+x=(4-2+1)x=3x$. Similarly, if we consider $(a+b)$ as a whole, then $4(a+b)-2(a+b)+(a+b)=(4-2+1)(a+b)=3(a+b)$. The mathematical idea used here is the "whole concept," which is an important thinking method in solving problems in secondary school teaching. It is widely used in the simplification and evaluation of polynomials.<br/>【Try to Apply】<br/>$(1)$ Considering $\left(a-b\right)^{2}$ as a whole, the result of combining $3\left(a-b\right)^{2}-6\left(a-b\right)^{2}+2\left(a-b\right)^{2}$ is ______;<br/>$(2)$ If $x^{2}-2y=4$, find the value of $23-3x^{2}+6y$;<br/>$(3)$ If $a-2b=3$, $2b-c=-5$, $c-d=-9$, 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}
user