
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 circle $O: x^{2}+y^{2}=3m^{2} (m > 0)$, and a parabola $C: y^{2}=2mx (m > 0)$. Let $P$ be the intersection point of circle $O$ and parabola $C$ in the fourth quadrant, and $N$ be the intersection point of circle $O$ with the negative half of the $y$-axis. The point $R$ is symmetric to point $N$ with respect to point $P$. Extend line $OR$ to intersect the parabola at point $Q$.

(Ⅰ) Find the ratio $\dfrac{|OR|}{|OQ|}$;

(Ⅱ) Determine how many intersection points there are between line $NR$ and the parabola, and provide a proof.

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