
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 following text and answer the questions.

Everyone knows that $\sqrt{2}$ is an irrational number, and irrational numbers are non-repeating infinite decimals. Therefore, we cannot write out the decimal part of $\sqrt{2}$ in its entirety. However, since $1 < \sqrt{2} < 2$, the integer part of $\sqrt{2}$ is $1$. Subtracting the integer part $1$ from $\sqrt{2}$, the difference is the decimal part $\sqrt{2}-1$. Based on the above content, answer the following questions:

$(1)$ The integer part of $\sqrt{5}$ is ______, and the decimal part is ______;  
$(2)$ The integer part of $1+ \sqrt{2}$ is ______, and the decimal part is ______;  
$(3)$ If the integer part of $2+ \sqrt{3}$ is $x$ and the decimal part is $y$, find the value of $x- \sqrt{3}y$.

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