
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
We know that $3a+5a-2a=(3+5-2)a=6a$. Similarly, when simplifying $4(a+b)+2(a+b)-(a+b)$, we can treat $a+b$ as a whole, then we have $4(a+b)+2(a+b)-(a+b)=(4+2-1)(a+b)=5(a+b)$.  
$(1)$ Treating $x+y$ as a whole, simplify the expression $3(x+y)^2-7(x+y)+8(x+y)^2+6(x+y)$;  
$(2)$ If $a^2+2a=3$, find the value of $3a^2+6a-14$;  
$(3)$ If $a-3b=3$, $2b+c=5$, $c-4d=-7$, find the value of the expression $\left(a-2b\right)-\left(3b-c\right)-\left(c+4d\right)$.

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