
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

In tetrahedron \(ABCD\), medians \(AM\) and \(DN\) are drawn on faces \(ACD\) and \(ADB\) respectively. Points \(E\) and \(F\) are taken on these medians such that \(EF \parallel BC\). Find the ratio \(EF : BC\).

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