
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 \( M \) is located on the lateral side \( AB \) of trapezoid \( ABCD \), such that \( AM : BM = 2 : 1 \). A line passing through point \( M \) parallel to the bases \( AD \) and \( BC \) intersects the lateral side \( CD \) at point \( N \). Find \( MN \), if \( AD = 18 \) and \( BC = 6 \).

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