
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 functions $f(x)=\frac{x}{\ln x}$ and $g(x)=\frac{x}{{x}^{2}-ex+{e}^{2}}$, if $\forall x\in \left(1,+\infty \right)$, the inequality $\left(t+1\right)\cdot g\left(x\right)\leqslant t\cdot f\left(x\right)$ holds for $t>0$, then the range of values for $t$ is ____.

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