
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:<br/>【Reading Material】It is now stipulated that the integer part and decimal part of a real number $x$ are represented by $\left[x\right]$ and $\left(x\right)$ respectively. For example, the integer part of the real number $3.14$ is $\left[3.14\right]=3$, and the decimal part is $\left(3.14\right)=0.14$; the integer part of the real number $\sqrt{5}$ is $[\sqrt{5}]=2$, the decimal part is an infinite non-repeating decimal, which cannot be fully written, but subtracting its integer part from it gives its decimal part, that is, $\sqrt{5}-2$ is the decimal part of $\sqrt{5}$, so $(\sqrt{5})=\sqrt{5}-2$.<br/>$(1)[\sqrt{3}]=$______,$(\sqrt{3})=\_\_\_\_\_\_.$<br/>$(2)$If $(\sqrt{7})=a,[\sqrt{37}]=b$, find the arithmetic square root of $a+b-\sqrt{7}$.

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