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

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

$(2)$ If $a\leq 0$, and $b=2a+1$, discuss the monotonicity of the function $f(x)$.

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