
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
Understanding and Thinking: Whole substitution is a mathematical thinking method. For example, if $x^{2}+x=0$, then $x^{2}+x+2023=\_\_\_\_.$<br/>We substitute $x^{2}+x$ as a whole, then the original expression $=0+2023=2023$.<br/>Following the above solution method, complete the following questions:<br/>$(1)$ If $m-n=-1$, find the value of $2\left(m-n\right)^{2}+18$;<br/>$(2)$ If $m^{2}+2mn=10$ and $n^{2}+3mn=6$, find the value of $2m^{2}+n^{2}+7mn$;<br/>$(3)$ When $x=-1$, the value of the algebraic expression $ax^{5}+bx^{3}+cx-5$ is $m$, find the value of the algebraic expression $ax^{5}+bx^{3}+cx-5$ when $x=1$ (please express it in an algebraic expression containing $m$).

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