
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
The diagonals of a convex quadrilateral are 12 and 18 and intersect at point \( O \).

Find the sides of the quadrilateral formed by the points of intersection of the medians of triangles \( AOB, BOC, COD \), and \( AOD \).

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