Should one who frequently experiences doubt about purity act upon the first thought that comes to mind, or is it obligatory for him to pause and reflect?

Whoever is overcome by doubt should act upon their first impression and disregard anything that comes after it. If their initial conviction is that they have completed something, they should proceed based on that. If their initial conviction is that they have not completed it, they should perform whatever they doubted about. The one afflicted by waswas (obsessive whispering) should act upon their first impression, such as in matters of purification (taharah) and circumambulation (tawaf).