
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 $4x-2x+x=(4-2+1)x=3x$. Similarly, if we consider $(a+b)$ as a whole, then $4(a+b)-2(a+b)+(a+b)=(4-2+1)(a+b)=3(a+b)$. The "whole concept" is an important thinking method in solving problems in secondary school teaching, and it is widely used in the simplification and evaluation of polynomials.  
$(1)$ Considering $(m-n)^{2}$ as a whole, the result of combining $3(m-n)^{2}-4(m-n)^{2}+3(m-n)^{2}$ is ______;  
$(2)$ Given $x^{2}+2y=4$, then the value of $3x^{2}+6y-2$ is ______;  
$(3)$ Given $x^{2}+xy=2$, $2y^{2}+3xy=5$, find the value of $2x^{2}+11xy+6y^{2}$.

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