How can I reenter the U.S. with a new green card and pending naturalization?

You must apply for a renewal of your green card (Form I-90). If you call USCIS with your I-90 receipt and an urgent need to travel, they may schedule you for an InfoPass appointment where you can receive a temporary I-551 stamp, which is evidence of your continuing LPR status. This will allow you to travel. If you leave the United States without the stamp, it will be more difficult. You will have to take your I-90 receipt notice to the U.S. embassy or consulate and ask for a boarding letter (Form I-131A) so you may board the plane to return to the United States.

File and I-90 green card renewal application and then make an InfoPass appointment to obtain a temporary stamp extending the card.

You may travel to the U.S. on an expired green card if you meet the criteria: you possess an expired permanent resident card with a 10-year expiration date. The airline may board you with the expired card, provided you meet all their other conditions for travel. Check with your airline or vessel before you buy a ticket or file Form I-131A. Or, second, a permanent resident card (with a two-year validity) and a Form I-797, notice of action, indicating that status is extended. Or if you have orders from the U.S. government (civilian or military) showing that time outside the U.S. was on official government business. These individuals should consult their air carrier prior to completion of an I-131A and payment of the fee.

You will be allowed to enter the U.S. You will be warned to renew the green card.

Yes, you will have trouble. You have to file for a replacement card and then when you get the receipt make an appointment with, get a temporary green card stamp.

Please do not travel abroad before getting this issue resolved. You could have serious difficulties on the border. The USCIS on its website says that if you are a permanent resident whose 10-year green card has expired or will expire within the next six months, you may begin the renewal process by online e-filing Form I-90, application to replace the permanent resident card. I strongly recommend you do this before you travel abroad.

You should not travel abroad with an expired permanent resident card. The safest thing to do is to file an extension application on Form I-90, and with your receipt, make an InfoPass appointment and get a temporary I-551 stamp.

Yes, get a stamp in your passport before leaving or file and I-90 for replacement card.

Yeah, I think you will. The expired green card may also give you problems in the citizenship process, which applying for does not automatically extend your permanent resident status. You need an immigration attorney to review this right away.

USCIS has been requiring naturalization applicants to maintain valid evidence of green card status. I would recommend you file an I-90 form to seek a replacement green card. The receipt will get you back into the U.S. and you will need to prove you filed for the new green card at your naturalization hearing anyway.

Seems like an InfoPass appointment is in order.