UX process for various products in different development phases

There are a lot of phases to go through in UX and UI design process. In research phase, there are various research methods available and many steps to take to achieve a meaningful result.

I would like to better understand, what UX research methods would be the most appropriate for projects in these cases?

1. Website

  • New website
  • Existing website - adding new pages, sections, updating any part, redesign

2. Web app

  • New web app

  • Existing web app - adding new pages, sections, updating any part, redesign

3. Mobile app

  • New mobile app

  • Existing mobile app - adding new pages, sections, updating any part, redesign

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