
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
Let the function $f(x)=(mx+n)\ln x$. If the tangent line of the curve $y=f(x)$ at point $P(e,f(e))$ (where $e$ is the base of the natural logarithm) is $y=2x-e$, then:

(Ⅰ) Find the intervals of monotonicity for the function $f(x)$;

(Ⅱ) If $a, b \in \mathbb{R}^{+}$, compare the size of $\dfrac{f(a)+f(b)}{2}$ and $f\left(\dfrac{a+b}{2}\right)$ and provide a proof.

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