Hello, my name is ***** ***** I will be the immigration attorney helping you today.
You can, but you need documentation to prove your status. To get this while it's pending, you should first make an infopass appointment at your local USCIS office. You can do that here https://infopass.uscis.gov/ - Just select "you need information" when it asks options. Print it out.
At the appointment, let the officer know that you need to travel and your N-400 is pending and your green card is expired. Bring your valid passport. They will stamp your passport with the I-551 to extend your green card so you can return to the US after travel. You will also take your expired green card on your trip.
Good luck to you during this process and I hope this answer has helped you!
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