
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
The function $f(x)=\left\{{\begin{array}{l}{{e^x}-a{x^2},x>0}\\{-{x^2}+({a-2})x+2a,x\leq 0}\end{array}}\right.$, if the solution set of the inequality $f\left(x\right)\geq 0$ with respect to $x$ is $\left[-2,+\infty \right)$, then the range of real number $a$ is ____.

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