
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 $f\left(x\right)=\ln x+ax^{2}-3x\left(a\in R\right)$.<br/>$(1)$ If the tangent line equation of the function $f\left(x\right)$ at the point $\left(1,f\left(1\right)\right)$ is $y=-2$, find the value of $a$;<br/>$(2)$ If $a=1$, for any $x_{1}$, $x_{2}\in \left[1,10\right]$, when $x_{1} \lt x_{2}$, the inequality $f({x}_{1})-f({x}_{2})＞\frac{m({x}_{2}-{x}_{1})}{{x}_{1}{x}_{2}}$ always holds, find the range of real number $m$.

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