Explanation:

- Determine: This means to establish or conclude after consideration. In the context of "new paths," it doesn’t fit as one doesn't typically determine paths on a trip.

- Deploy: This means to strategically position or arrange. It's more often used in a military or technical context, not when referring to personal exploration or travel.

- Invent: This means to create something that hasn't existed before. While you can invent new ideas or tools, you wouldn't typically invent paths.

- Explore: This means to travel through to learn about or familiarize oneself with a place. It is perfectly suited for a trip focused on discovering new paths.