
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 $f(x) = \ln x$ and $g(x) = (2m+3)x + n$, if for any $x \in (0, +\infty)$, it always holds that $f(x) \leq g(x)$, denote the minimum value of $(2m+3)n$ as $f(m, n)$, determine the maximum value of $f(m, n)$.

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