
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 a math class, the teacher posed a question: "By exploring, we know that $\sqrt{2}\approx 1.414\ldots $, it is an infinite non-repeating decimal, also known as an irrational number. Its integer part is $1$. Can anyone tell me what its decimal part is?" Xiao Ming raised his hand and answered, "We cannot write out its decimal part completely, but we can represent its decimal part as $\sqrt{2}-1$." Teacher Zhang praised Xiao Ming for being very clever and affirmed his statement. Now, please answer the following based on Xiao Ming's statement:<br/>$(1)$ If the decimal part of $\sqrt{5}$ is $a$, and the integer part of $\sqrt{37}$ is $b$, find the value of $a+b-\sqrt{5}$.<br/>$(2)$ Given $8+\sqrt{3}=x+y$, where $x$ is an integer and $0 \lt y \lt 1$, find the value of $3x+{(y-\sqrt{3})}^{2023}$.

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