
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 functions $f(x)=e^{x}$, where $x\in R$, and $g(x)=\ln x$, where $x\in(0,+\infty)$.

(I) If the line $y=kx+2$ is tangent to the graph of $g(x)$, find the value of the real number $k$.

(II) Discuss the number of common points of the curve $y=f(x)$ and the curve $y=mx^{2}$ (where $m > 0$) when $x > 0$.

(III) Given $a < b$, compare the sizes of $\frac{f(a)+f(b)}{2}$ and $\frac{f(b)-f(a)}{b-a}$, and explain the reason.

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