
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 line defined by the parametric equations $\begin{cases} x=2-t\sin 30^{\circ} \\ y=-1+t\sin 30^{\circ} \end{cases}$ and the circle ${x}^{2}+{y}^{2}=8$, the line intersects the circle at points $B$ and $C$. Point $O$ is the origin. Calculate the area of triangle $BOC$.

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