
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
Point \( M \) divides the midline of triangle \( ABC \), parallel to side \( BC \), into segments, one of which is three times longer than the other. Point \( N \) divides side \( BC \) into segments, one of which is three times longer than the other. In what ratio does the straight line \( MN \) divide the area of triangle \( ABC \)?

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