
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 a quadratic equation in $x$, $mx^{2}-2x+1=0$.<br/>$(1)$ If the equation has two real roots, find the range of $m$;<br/>$(2)$ If the two real roots of the equation are $x_{1}$ and $x_{2}$, and $x_{1}\cdot x_{2}-x_{1}-x_{2}=\frac{1}{2}$, find the value of $m$.

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