
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 $f(x)=2x+\frac{1}{{x}^{2}}-4$, and the function $g(x)=\frac{lnx}{x}-m$. If for any $x_{1}\in \left[1,2\right]$, there exists $x_{2}\in [\frac{1}{e}$,$e^{2}]$ such that $f(x_{1})\leqslant g(x_{2})$, then the range of real number $m$ is ______.

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