
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 curve $\begin{cases} x = 2 - t \sin 30^{\circ} \\ y = -1 + t \sin 30^{\circ} \end{cases}$ (where $t$ is a parameter) intersects with the curve $\rho = 2 \sqrt{2}$ at points $B$ and $C$, find the value of $|BC|$ (the distance between $B$ and $C)$.

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