
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 $f(x)=(x-2){e}^{x}-\frac{a}{2}({x}^{2}-2x)$.<br/>$(1)$ When $a=e$, find the maximum value of the function $f(x)$ on the interval $\left[1,2\right]$;<br/>$(2)$ If $f(x)$ has a local maximum point $x_{0}$ and $f(x_{0}) \lt 0$, find the range of values for $a$.

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