
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 when calculating $5x-2x+x$, we can solve it like this: $5x-2x+x=(5-2+1)x=4x$.<br/>【Analogous Imitation】Using a similar method as the reading material, we can treat $\left(5m+2\right)$ as a whole: $5\left(5m+2\right)-2\left(5m+2\right)+\left(5m+2\right)=(5-2+1)\times \left(5m+2\right)=4\left(5m+2\right)$<br/>【Application Attempt】Following the solution method above, complete the following questions.<br/>$(1)$ Given $x^{2}-2x=5$, find the value of $2x^{2}-4x+2023$;<br/>$(2)$ Given $m-n=-3$, find the value of $2\left(m-n\right)-m+n+5$;

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