Heat olive oil in a large pot over medium heat. Add plantains and potatoes; fry until crisp outside, about 5-7 minutes. Remove from pot and set aside, reserving oil.
Cook onion and garlic in the same oil until onion is translucent, 5-7 minutes. Add chicken and sausage; season with salt and pepper. Cover and cook for 5 minutes.
Add enough water to cover chicken completely. Bring to a simmer, then cook for 10 more minutes. Stir in tomatoes, cover, and cook another 10 minutes.
Add the reserved plantains, potatoes, garbanzo beans, and cabbage. Cook covered until cabbage wilts and all is hot, about 5 minutes.
Serve hot
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