
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 $f(x)=ax^2+bx+x\ln x$, the equation of the tangent line at the point $(1,f(1))$ is $3x-y-2=0$.  
(1) Find the values of the real numbers $a$ and $b$;  

(2) Let $g(x)=x^2-x$, if $k\in \mathbb{Z}$, and $k(x-2) < f(x)-g(x)$ holds for any $x > 2$, find the maximum value of $k$.

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