
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 $f(x)=ax^2-bx+\ln x, a,b\in R$.

(1) When $a=b=1$, find the equation of the tangent line to the curve $y=f(x)$ at $x=1$;

(2) When $b=2a+1$, discuss the monotonicity of the function $f(x)$;

(3) When $a=1, b > 3$, let the two zeros of the derivative function $f'(x)$ be $x_1$ and $x_2$ ($x_1 < x_2$).

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