
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
## Analysis

This problem examines the method of solving issues where an inequality is always true. It emphasizes the application of the method for finding the minimum value of a quadratic function and solving quadratic inequalities. It also tests the judgment of the truth of propositions, as well as transformation and calculation abilities, making it a medium-difficulty question.

Given that for any $x \in \mathbb{R}$, the inequality $x^{2}-2x-1 \geqslant m^{2}-3m$ is always true, by applying the method for finding the minimum value of a quadratic function, we can obtain $m^{2}-3m \leqslant -2$. Solving this inequality will give us the range of $m$. When the proposition $\neg p$ is true, then $P$ is false, which allows us to determine the range of $m$.

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