If something takes a full day, it requires your undivided attention for the entire day. If you spend more than 1 hour doing anything else while attempting an action that requires a full day (except meals and short rest breaks) besides that action, that day cannot be counted towards your progress.
If you have spells, feats, magic items, or abilities, which can grant you a boost to the action you are performing, these things may only be used if the duration of the bonus provided lasts the full day (i.e. 'until the next full night's rest'). Spells, feats, magic items, or abilities with durations less than this may not be used, even if you can recast them multiple times.