
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 a function $f(x)=a{e^x}-\frac{1}{2}{x^2}$, where $a\in\mathbb{R}$. If the function has two critical points $x_{1}$ and $x_{2}$, and $\frac{x_{2}}{x_{1}}\geq 2$, then the range of real number $a$ is ____.

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