
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 "whole idea" is an important thinking method in solving high school mathematics problems, and it is widely used in the simplification and evaluation of polynomials. For example, $4a-2a+a=\left(4-2+1\right)a=3a$. Similarly, if we consider $\left(x+y\right)$ as a whole, then $4\left(x+y\right)-2\left(x+y\right)+\left(x+y\right)=\left(4-2+1\right)\left(x+y\right)=3\left(x+y\right)$. Please follow the above problem-solving method to complete the following questions:<br/>【Try to Apply】<br/>$(1)$ Considering $\left(x-y\right)^{2}$ as a whole, merge $3\left(x-y\right)^{2}-6\left(x-y\right)^{2}+2\left(x-y\right)^{2}$, the result is______.<br/>$(2)$ Given $a^{2}-2b=2$, find the value of $4a^{2}-8b-9$.<br/>【Further Exploration】<br/>$(3)$ Given $a-2b=4$, $b-c=-5$, $3c+d=10$, find the value of $\left(a+3c\right)-\left(2b+c\right)+\left(b+d\right)$.

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