
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 $f(x)=x\ln x$ and $g(x)= \frac {a}{2}x^{2}+x-a$ $(a\in\mathbb{R})$.

(Ⅰ) If the line $x=m$ $(m > 0)$ intersects the curves $y=f(x)$ and $y=g(x)$ at points $M$ and $N$ respectively, let the tangent line to $y=f(x)$ at point $M$ be $l_{1}$, and the tangent line to $y=g(x)$ at point $N$ be $l_{2}$.

(i) When $m=e$, if $l_{1} \perp l_{2}$, find the value of $a$;

(ii) If $l_{1} // l_{2}$, find the maximum value of $a$;

(Ⅱ) Let the function $h(x)=f(x)-g(x)$ have exactly two different extreme points $x_{1}$ and $x_{2}$ in its domain, with $x_{1} < x_{2}$. If $\lambda > 0$, and $\lambda\ln x_{2}-\lambda > 1-\ln x_{1}$ always holds, find the range of $\lambda$.

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