
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 $f(x)=\frac{1}{3}{x}^{3}-2x+{e}^{x}-\frac{1}{{e}^{x}}$, where $e$ is the base of natural logarithm. If $f\left(2a-3\right)+f(a^{2})\leqslant 0$, then the range of real number $a$ is ______.

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