The most appropriate phrase for the underlined segment in the given sentence is "came up with". It means to think of or invent something new. In this case, the woman thought of new ideas for the innovative promotion of the product.
The other options are incorrect.
- Draw on means to use something as a source of inspiration or information.
- Swept off means to be impressed or charmed by someone or something.
- Carry off means to succeed in doing something difficult or challenging.
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