
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 $f\left(x\right)=(2ae^{x}-x)e^{x}$.<br/>$(1)$ If $a=0$, find the monotonic interval of $f\left(x\right)$;<br/>$(2)$ If for any $x\in R$, $f(x)+\frac{1}{a}≤0$ always holds, find the minimum value of $a$.

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