
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 mathematical problem solving, and it is widely used in the simplification and evaluation of polynomials. We know that $4x-2x+x=(4-2+1)x=3x$. Similarly, we can consider $\left(a+b\right)$ as a whole, then $4\left(a+b\right)-2\left(a+b\right)+\left(a+b\right)=(4-2+1)\left(a+b\right)=3\left(a+b\right)$. Please try to solve:<br/>$(1)$ Consider $\left(a-b\right)^{2}$ as a whole, combine $3\left(a-b\right)^{2}-6\left(a-b\right)^{2}+2\left(a-b\right)^{2}=$______;<br/>$(2)$ Given $x^{2}-2y=4$, find the value of $3x^{2}-6y-21$;<br/>$(3)$ Given $a-5b=3$, $5b-3c=-5$, $3c-d=10$, find the value of $\left(a-3c\right)+\left(5b-d\right)-\left(5b-3c\right)$.

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