
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 $f(x)=xe^{x}- \frac {1}{2}(a+1)(x^{2}+2x)$, $g(x)=\ln x- \frac {1}{2}(a+1)x^{2}-ax+a+1$, where $a\in\mathbb{R}$.  
$(1)$ Discuss the monotonicity of $f(x)$;  
$(2)$ When $x > 0$, there exists a point on the graph of the function $y=f(x)$ that is below the graph of the function $y=g(x)$. Find the range of values for $a$.

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