(a) The party intending to move for a new trial shall file with the clerk and serve upon each adverse party a notice of their intention to move for a new trial, designating the grounds upon which the motion will be made and whether the same will be made upon affidavits or the minutes of the court, or both, either:

1. (1) After the decision is rendered and before the entry of judgment.
2. (2) Within 15 days of the date of serving notice of entry of judgment by the clerk of the court pursuant to Section 664.5, or service upon them by any party of written notice of entry of judgment, or within 180 days after the entry of judgment, whichever is earliest; provided, that upon the filing of the first notice of intention to move for a new trial by a party, each other party shall have 15 days after the service of that notice upon them to file and serve a notice of intention to move for a new trial.