The auditors have audited a client's cryptoassets. Those assets originally cost $$100,000$ in $20$X$1,$ but in $20$X$3$ were judged as impaired and reported on the financial statement at $$80,000.$ This year, the estimated fair value of the cryptoassets is $$85,000.$ Under GAAP, the auditors would expect the proper valuation of the account is most likely to be:

$(1)$ $ $80,000.$

$(2)$ $ $82,500.$

$(3)$ $ $85,000.$

$(4)$ $$100,000$