
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: "Holistic Thinking" is an important thinking method in solving high school mathematics problems. It is widely used in the simplification and evaluation of polynomials. We know that $7x-5x+x=\left(7-5+1\right)x=3x$. Similarly, if we consider $\left(a+b\right)^{2}$ as a whole, then $7\left(a+b\right)^{2}-5\left(a+b\right)^{2}+\left(a+b\right)^{2}=\left(7-5+1\right)\left(a+b\right)^{2}=3\left(a+b\right)^{2}$.  
$(1)$ Try to apply: Considering $\left(a-b\right)^{4}$ as a whole, the result of combining $10\left(a-b\right)^{4}-25\left(a-b\right)^{4}+5\left(a-b\right)^{4}$ is ______;  
$(2)$ Given $2x^{2}-3y=8$, find the value of $4x^{2}-6y-32$;  
$(3)$ Further exploration: Given $a^{2}+2ab=-5$, $ab-2b^{2}=-3$, find the value of the expression $3a^{2}+4ab+4b^{2}$.

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