
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
A student research group at a school found that the attention index of students during class changes with the listening time. At the beginning of the lecture, students' interest surges; then, their interest remains in a relatively ideal state for a while, after which students' attention begins to disperse. Let $f(x)$ represent the student attention index, which changes with time $x$ (minutes) (the larger $f(x)$, the more concentrated the students' attention). The group discovered the following rule for $f(x)$ as time $x$ changes: 
$$f(x)= \begin{cases} 100a^{ \frac {x}{10}}-60, & (0\leqslant x\leqslant 10) \\ 340, & (10 < x\leqslant 20) \\ 640-15x, & (20 < x\leqslant 40)\end{cases}$$
where $a > 0, a\neq 1$.  
If the attention index at the 5th minute after class starts is 140, answer the following questions:  
(Ⅰ) Find the value of $a$;  
(Ⅱ) Compare the concentration of attention at the 5th minute after class starts and 5 minutes before class ends, and explain the reason.  
(Ⅲ) During a class, how long can the student's attention index remain at least 140?

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