
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
Scientific research shows that in general, students' attention changes with the teacher's lecture time in a 40-minute class. At the beginning of the class, students' attention gradually increases, and then their attention begins to disperse. Through experimental analysis, it is found that the index of students' attention $y$ changes with time $x$ (minutes) according to the following rules: $y=f\left(x\right)=\left\{\begin{array}{}2x+68,0\leqslant x \lt 8 \\ -\dfrac{1}{8}\left(x^{2}-32x-480\right),8\leqslant x\leqslant 40\end{array}\right.$

(1) If the index of students' attention is not less than 80, it is called the "ideal listening state". How long does a student stay in the "ideal listening state" during a 40-minute class? (Round to the nearest minute)

(2) There is a key math question that the teacher must explain continuously for 24 minutes. In order to achieve better results, it is required that the minimum value of students' attention index during these 24 minutes is maximized. Then, from which minute after the teacher starts the class should the teacher begin explaining this question? (Round to the nearest minute)

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