
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
Given the function $f(x) = e^x$, where $x \in \mathbb{R}$:
(Ⅰ) If the line $y=kx+1$ is tangent to the graph of the inverse of $f(x)$, find the value of the real number $k$;
(Ⅱ) Let $x>0$, discuss the number of common points between the curve $y=\frac{f(x)}{x^2}$ and the line $y=m$ ($m>0$);
(Ⅲ) Let $a < b$, compare the values of $f\left(\frac{a+b}{2}\right)$ and $\frac{f(b)-f(a)}{b-a}$, and explain the reasons.

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