
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 $f(x)=\ln x-mx^{2}-x$.
(1) If $x=\dfrac{1}{2}$ is an extreme point of $f(x)$, find the maximum value of $f(x)$.
(2) If for all $x_1, x_2 \in \left[\dfrac{1}{e}, e\right]$ with $x_1 \neq x_2$, the inequality $x_2 f(x_1) - x_1 f(x_2) > x_1 x_2 (x_2 - x_1)$ holds, find the range of real numbers $m$.

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