Grammatically correct; however, you won't be understood. "I am taking..." and "I was going to take.." both have correct verb conjugation but "my cycle" does not make sense as a noun in this context. If you are referring to bicycling, you can say bicycling, biking, or cycling as a verb. As a noun it only works as bicycle or bike for short. The word "cycle" as a noun doesn't refer to bicycling which is why your sentence is confusing. Cycle as a noun means a series of events. With this in mind, if you keep the subject and verb in your original sentence you could say: I am taking out my bicycle // I was going to take out my bicycle - (as in you are/were about to use bicycle). I am cycling or I was going to bike. (You are/were doing the action of bicycling

both are correct

If you are talking about the future then the first sentence is correct☺️

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