
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 diagonals AC and BD of a parallelogram intersect at point O, and let CO, BN, and DM be medians of triangle BCD intersecting at point K. By the property of medians, BK:KN = 2:1. Since DM is perpendicular to AC, triangle CKD is right-angled. KN is its median drawn to the hypotenuse, making KN = 1/2 CD. Thus, BN:CD = 3:2. Given BN = 1.5 CD = 9.

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