
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 four points \(A, B, C,\) and \(D\) that are not coplanar, in what ratio does the plane passing through the intersection points of the medians of triangles \(ABC\), \(ABD\), and \(BCD\) divide the segment \(BD\)?

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