When you consider or examine something again, you reevaluate it. If a child catches her dad leaving a quarter under her pillow, it will make her reevaluate her belief in the Tooth Fairy.
You might think the story you wrote is pretty terrible, but if your favorite English teacher disagrees, you might reevaluate it, or read it again with an open mind. Your dentist may say she doesn't see any cavities, but if you describe the ache in your tooth, she may reevaluate your x-rays. Evaluate comes from the French évaluer, "to find the value of," and reevaluate adds the "again" prefix re-.