
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
(1) The volume of a cube is $8cm^{3}$. The volume of the circumscribed sphere of this cube is _______ $cm^{3}$.

(2) Let $A=\{x|x^{2}-3x-10\leqslant 0\}$, $B=\{x|m+1\leqslant x\leqslant 2m-1\}$. If $A\bigcap B=B$, then the range of values for the real number $m$ is _______.

(3) Given the function $f(x)=\begin{cases}(2a-1)x+7a-2, & x < 1 \\ a^{x}, & x\geqslant 1\end{cases}$ is monotonically decreasing on $\mathbb{R}$, then the range of values for the real number $a$ is _______.

(4) Given planes $\alpha, \beta$, and lines $m, n$, with $m\bot \alpha$, $n\subseteq \beta$, consider the following four statements:

$\quad$① If $\alpha \parallel \beta$, then $m\bot n$;    

$\quad$② If $m\bot n$, then $\alpha \parallel \beta$;

$\quad$③ If $m\parallel n$, then $\alpha \bot \beta$;    

$\quad$④ If $\alpha \bot \beta$, then $m\parallel n$;

The correct statements are _______.

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