
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 an ellipse \(\frac{x^{2}}{4} + y^{2} = 1\) and three points \(A, B, C\) on it, the line \(BC\) with a negative slope intersects the \(y\)-axis at point \(M\). If the origin \(O\) is the centroid of triangle \(\triangle ABC\), and the area ratio of triangles \(\triangle BMA\) to \(\triangle CMO\) is \(3:2\), determine the slope of line \(BC\).

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