
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 function $f(x)= \frac{a}{2}x^{2}+(x+1)e^{-x}-1$  
$(1)$ Discuss the monotonic intervals of the function $f(x)$;    

$(2)$ If $e^{x}- \frac{a}{2}x^{2}e^{|x|} \leqslant x+1$, find the range of values for $a$.

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