
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 $f(x)=\frac{1}{3}{x}^{3}-{x}^{2}-x+{e}^{x}-\frac{1}{{e}^{x}}$, where ${f'}\left(x\right)$ is the derivative of $f\left(x\right)$, if the inequality $f(3a^{2}-2a-1)\leqslant {f'}\left(x\right)+2x-1$ holds for all $x\in R$, then the range of real number $a$ is ______.

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