
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 $f(x)=mx^{2}-x+\ln x$.

$(1)$ If there exists an interval $D$ within the domain of function $f(x)$, such that the function is decreasing on interval $D$, find the range of the real number $m$.

$(2)$ When $0 < m \leqslant \frac{1}{2}$, if the tangent line $l$ at point $x=1$ of curve $C$: $y=f(x)$ has only one common point with curve $C$, find the value or range of $m$.

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