
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
The essence of learning is self-study. On the weekend, after reviewing the completing the square method, student Xiao Rui expanded the algebraic expression $x^{2}+4x+6$ and found that $x^{2}+4x+6=x^{2}+4x+4+2=\left(x+2\right)^{2}+2$. Xiao Rui noticed that $\left(x+2\right)^{2}$ is a non-negative number, meaning $\left(x+2\right)^{2}\geqslant 0$. He continued to explore and using the basic properties of inequalities, he deduced that $\left(x+2\right)^{2}+2\geqslant 0+2=2$, which implies $\left(x+2\right)^{2}+2\geqslant 2$. Therefore, he concluded that the minimum value of $\left(x+2\right)^{2}+2$ is $2$, and consequently, the minimum value of $x^{2}+4x+6$ is $2$. Xiao Rui then attempted to find the extreme values of a quadratic trinomial using the completing the square method and designed two questions for you to solve.<br/>$(1)$ Find the minimum value of the algebraic expression $m^{2}-6m+10$.<br/>$(2)$ Find the extreme values of the algebraic expression $-2x^{2}-4x+3$.

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