
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: Use $\left[x\right]$ and $\left(x\right)$ to represent the integer part and decimal part of a real number $x$, such as the integer part of the real number $3.14$ is $\left[3.14\right]=3$, and the decimal part is 〈$3.14$〉$=0.14$; the integer part of the real number $\sqrt{7}$ is $[\sqrt{7}]=2$, and the decimal part is an infinite non-repeating decimal, which cannot be written completely, but subtracting its integer part from it equals its decimal part, that is, $\sqrt{7}-2$ is the decimal part of $\sqrt{7}$, so $(\sqrt{7})=\sqrt{7}-2$.<br/>$(1)[\sqrt{2}]=$______,$(\sqrt{2})=$______；$[\sqrt{11}]=$______,$(\sqrt{11})=$______；<br/>$(2)$If $(\sqrt{5})=a$,$[\sqrt{101}]=b$, find the cube root of $a+b-\sqrt{5}$.

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