
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's draw the diagonals AC and BD of the parallelogram. Let them intersect at point O. Then CO, BN, DM are medians of triangle BCD. Let them intersect at point K. By the property of medians, BK:KN = 2:1. Since DM is perpendicular to AC, triangle CKD is a right triangle. KN is the median drawn to the hypotenuse. Therefore, KN = 1/2 CD. Then BN:CD = 3:2. Thus, BN = 1.5 CD = 9.

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