
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 $x=t$ $(t > 0)$ intersects the curves $y=f(x)$ and $y=g(x)$ at points $A$ and $B$ respectively, and the tangent line to $y=f(x)$ at point $A$ is parallel to the tangent line to $y=g(x)$ at point $B$, find the range of values for $a$;
(II) Let $h(x)=f(x)-g(x)$, suppose there are two distinct extremal points $x_1$ and $x_2$ in its domain with $x_1 < x_2$, and for a given $\lambda > 0$, if the inequality $e^{1+\lambda} < x_1 \cdot x_2^\lambda$ always holds, find the range of values for $\lambda$.

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