When the twenty-seven minutes are up, you should stop working on the paragraph and take a break for three minutes. You will soon discover whether a three minute break is enough. There is no shame in organizing your process into 26 minute sessions plus 4-minute breaks, or 25 + 5. Whatever works for you. As long as the break isn't so long that your prose gets cold. After the break, you continue with the next thing you've got planned for that day. That may be writing another paragraph, or it may be some reading or analysis to prepare for tomorrow's writing sessions, or it may be something completely unrelated to what you're writing. The important thing is to have some specific task to move on to. The writing of this particular paragraph is, in any case, over now. Don't leave yourself an opening to keep struggling with it. You'll have a chance to work on it again further down the road.
If the next thing happens to be writing another paragraph, start, as I suggested on Monday, by typing out the key sentence. Notice that this means that the next thing you're writing has a very clear focus, and this sequence of shifts of focus is something you were aware of the night before.*
People are different and their writing processes may benefit from different ways of working through their material. Imagine three writers who have each set aside ten hours, two hours a day, in a given week. That means they will each write 20 paragraphs in all, 4 paragraphs a day. That's half a paper. Now, Writer A may write the introduction and the first paragraph of the conclusion on Monday, then the first paragraph of the background, theory, methods, and analysis section on Tuesday. Then the second paragraph of each of these sections on Wednesday, until there are four paragraphs in each section by the end of Friday's writing. Writer B, by contrast, may write four paragraphs for each section in a row. Writer C, finally, might write the three paragraphs of the introduction and the first paragraph of the background on Monday, continuing with the remaining four paragraphs of the background on Tuesday, and the first four paragraphs of theory on Wednesday. By the end of the week, Writer C has written the first 20 paragraphs of the paper in sequence. Whatever works.
*I should perhaps clarify that many writers prefer to establish this awareness immediately after their writing is finished for the day. Others like to reflect on tomorrow's writing tasks before they leave the office in the afternoon. Some do it in the evenings, after closing the book they're reading. And some, finally, glance at the key sentences for the morning to come just before they put their head on the pillow and go to sleep. Whatever works. What I mean is that you should know what you're writing tomorrow at the latest before you go to sleep.