
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 functions $f(x)= \dfrac{\ln x}{x}$ and $g(x)=-ex^2+ax$ (where $e$ is the base of natural logarithms), for any $x_1 \in \mathbb{R}$, there exists $x_2 \in \left[ \frac{1}{3}, 2 \right]$ such that $f(x_1) \leqslant g(x_2)$. Determine the range of values for $a$.

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