
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 hyperbola $C$: $\frac{x^{2}}{3}-y^{2}=1$, with $O$ being the origin and $F$ the right focus of $C$. A line passing through $F$ intersects the two asymptotes of $C$ at points $M$ and $N$, respectively. If $\triangle OMN$ is a right-angled triangle, then calculate the length of $|MN|$.

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