
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
In algebraic expression evaluation problems, the overall concept is widely used, such as: given the algebraic expression $5a+3b=-4$, find the value of the algebraic expression $2\left(a+b\right)+4\left(2a+b\right)+3$. The solution is as follows: The original expression $=2a+2b+8a+4b+3=10a+6b+3=2\left(5a+3b\right)+3=2\times \left(-4\right)+3=-5$. Using the overall concept, complete the following problems:  
$(1)$ Given $-m^{2}=m$, then $m^{2}+m+1=$______;  
$(2)$ Given $m-n=2$, find the value of $2\left(n-m\right)-4m+4n-3$;  
$(3)$ Given $m^{2}+2mn=-2$, $mn-n^{2}=-4$, find the value of $3m^2+\frac{9}{2}mn+\frac{3}{2}n^2$.

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