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Palm Seeds and Fronds and general green waste removal

We have a palm tree which had seeded. We cut down some fronds and the seed baskets (don’t know how to describe them) and I put them in my green waste bin only to google to find out I can’t dispose them via our TCC green bin. I would really appreciate if someone could take the rubbish from our green bin and dispose of it as required and I’m a bit lost on what to do. Timing wise, it would be great for it to be done asap as I have more gardening to do but have no space left in my green bin ie. in the next 2 weeks ideally. Thanks so much! Sophia