When it comes to describing an innovative approach to something, there are a plethora of synonyms available at your disposal. Some possible alternatives to "innovatively" could include: creatively, ingeniously, resourcefully, imaginatively, inventively, originatively, unconventionally, and cutting-edge. Each of these words conveys a similar message of coming up with new and fresh ideas, but they may emphasize different aspects of the innovative process. For example, one might use "creatively" to suggest a highly imaginative approach, while "unconventionally" might describe a fresh take on a well-worn topic. Ultimately, the precise synonym you choose will depend on the context and tone of your writing or speaking.