If you do not agree that you abandoned your residence, do not sign anything and ask for a hearing with an immigration judge
The CBP may try to have you sign an abandonment of residence Form I-407. They will occasionally try and bully people into signing, sometimes threatening detention. If you want to retain your resident status, you should politely refuse to sign anything and ask that they issue a Notice to Appear (NTA). Often LPR's will have more of a chance to establish that they did not abandon their residence in front of an immigration judge.
Carry proof of non-abandonment with you on your trip
To maintain resident status, you must continue to have the U.S. as your principal place of residence. If you expect to be outside the U.S. you can indicate an intent to maintain resident status by obtaining a Reentry Permit, which can allow readmission to the U.S. for up to 2 years. You should also continue to file income taxes and carry copies of the forms with you, maintain bank accounts, show school records of children who remained in the U.S., drivers licenses from the U.S., proof of home ownership, and other documentation showing you did not depart with the intention of abandoning your the LPR.
Contact an experienced immigration attorney
You may also call an immigration attorney who can request that CBP defer your inspection to provide additional evidence of nonabandonment, or represent you in a removal proceeding before an immigration judge. Since the government is charging you being removeable from the U.S., it is advisable to have competent representation.