
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 $f(x)=\ln(x)+x^{2}-ax$ (where $a$ is a constant),

(1) If $x=1$ is an extremum point of the function $f(x)$, find the value of $a$;

(2) When $0 < a \leqslant 2$, determine the monotonicity of $f(x)$;

(3) If for any $a \in (1,2)$, and $x_{0} \in [1,2]$, the inequality $f(x_{0}) > m\ln(a)$ always holds, find the range of the real number $m$.

Candidates should choose either question 22 or 23 to answer. If both questions are answered, only the first one will be graded. When answering, please darken the corresponding question number on the answer sheet with a 2B pencil.

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