
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 $f(x)=\ln x+x^{2}-2ax+1$ (where $a$ is a constant),  
(1) Discuss the monotonicity of the function $f(x)$;  
(2) If for any $a\in(1, \sqrt {2})$, there exists $x_{0}\in(0,1]$ such that the inequality $f(x_{0})+\ln a > m(a-a^{2})$ holds, find the range of the real number $m$.

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