
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 $f(x)={e}^{x}-\frac{1}{2}a{x}^{2}-x$.  
$(1)$ If $f(x)$ is monotonically increasing, find the value of $a$.  
$(2)$ Determine the relationship between $(1+1)(1+\frac{1}{4})⋅⋅⋅(1+\frac{1}{{n}^{2}})$ (where $n\in N^{*}$ and $n\geqslant 2$) and $e^{2}$, and explain the reason.

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