
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
Let $m$ be a real number. The line $y = mx + 1$ intersects the circle $C: x^{2} - x + y^{2} = 0$ at points $P$ and $Q$. <br/>$(1)$ If $PQ = \frac{{\sqrt{2}}}{2}$, find the value of $m$; <br/>$(2)$ Point $O$ lies outside the circle with diameter $PQ$ (where $O$ is the origin), find the range of values of $m$.

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