
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
Let \(A, B, C\), and \(D\) be four points that are not coplanar. A plane passes through the centroid of triangle \(ABC\) that is parallel to the lines \(AB\) and \(CD\). In what ratio does this plane divide the median drawn to the side \(CD\) of triangle \(ACD\)?

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