
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
Math teacher Zhang posed a question in class: "Through exploration, we know that $\sqrt{2}≈1.414⋯$. 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 questions based on Xiao Ming's explanation:<br/>$(1)$ What is the decimal part of $\sqrt{3}$? Please express it;<br/>$(2)$ Let $a$ be the decimal part of $\sqrt{3}$, $b$ be the integer part of $\sqrt{5}$. Find the value of $a+b-\sqrt{3}$;<br/>$(3)$ Given $8+\sqrt{3}=x+y$, where $x$ is a positive integer, $0 \lt y \lt 1$, find the value of $2x+{({y-\sqrt{3}})^{2023}}$.

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