
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
Read the comprehension and solve the problem:<br/>"Holistic thinking" is an important concept in high school mathematics, running through the entire process of high school mathematics, such as holistic substitution, holistic substitution, holistic reduction, holistic summation, holistic construction, $\ldots $, some problems are difficult to solve if approached locally and taken apart, but looking at the whole picture and thinking holistically can simplify the problem, make it easier, and solve complex problems easily.<br/>Example: When the algebraic expression $x^{2}+3x+5$ equals $7$, find the value of the algebraic expression $3x^{2}+9x-2$.<br/>Solution: Because $x^{2}+3x+5=7$, then $x^{2}+3x=2$.<br/>Therefore, $3x^{2}+9x-2=3(x^{2}+3x)-2=3\times 2-2=4$.<br/>The above method is a typical holistic substitution method.<br/>According to the reading material, please solve the following problems:<br/>$(1)$ Given $a^{2}+3a-2=0$, find the value of $5a^{3}+15a^{2}-10a+2020$.<br/>$(2)$ We know that the solutions to the equation $x^{2}+2x-3=0$ are $x_{1}=1$ and $x_{2}=-3$. Now, given another equation $\left(2x+3\right)^{2}+2\left(2x+3\right)-3=0$, the solutions are ______.

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