
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: The overall idea is an important thinking method in mathematical problem solving, widely used in polynomial simplification and evaluation applications. For example, viewing $\left(a+b\right)$ as a whole, $3\left(a+b\right)-2\left(a+b\right)+\left(a+b\right)=\left(3-2+1\right)\left(a+b\right)=2\left(a+b\right)$. Answer the following questions based on the above method:<br/>$(1)$ Simplify using the overall idea: $2\left(a-b\right)^{2}-4\left(a-b\right)^{2}+7\left(a-b\right)^{2}$;<br/>$(2)$ If $a^{2}-2b^{2}-3=0$, find the value of $-3a^{2}+6b^{2}+2032$;<br/>$(3)$ Given: $a^{2}+2ab=15$, $b^{2}+2ab=6$, find the value of the algebraic expression $2a^{2}-4b^{2}-4ab$.

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