
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 $f(x)=\ln x - ax$ and $g(x)=e^{x} - 3ax$, where $a$ is a real number, find the range of values for $a$ such that $f(x)$ is a monotonically decreasing function on $(1, +\infty)$ and $g(x)$ has a minimum value on $(1, +\infty)$.

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