
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 $f(x)\leqslant g(x)$ holds true for any $x\in(0,+\infty)$, let the minimum value of $(2m+3)n$ be denoted 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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