
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
Since $\sqrt[3]{1}＜\sqrt[3]{3}＜\sqrt[3]{8}$, that is, $1＜\sqrt[3]{3}＜2$, so the integer part of $\sqrt[3]{3}$ is $1$, and the decimal part is $\sqrt[3]{3}-1$. By analogy, answer the following questions:<br/>$(1)$ Find the integer part and decimal part of $\sqrt[3]{30}$;<br/>$(2)$ If $m$ is the integer part of $7-\sqrt[3]{20}$, and $\left(x+1\right)^{2}=m$, find the value of $x$.

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