By Howard SchneiderWASHINGTON, Aug 11 (Reuters) - U.S. consumers took out a record amount in auto loans in the second quarter and boosted their credit card and home equity balances as well, the New York Fed said in its latest household debt and ‌credit report on Tuesday. The overall delinquency ‌rate fell in the second quarter in a sign ⁠that household balance sheets on average remain resilient despite a decline in inflation-adjusted incomes. In a blog post accompanying the New York Fed's report, staff economists said credit card delinquency rates in particular, while still elevated compared to the period before ⁠the pandemic, appear to have stabilized. An increase in the share of credit card debt more than 90 days past due, from 7.6% in late 2022 to 12.8% at the start of this year, prompted concerns about deteriorating household finances. Overall delinquency on all forms of credit fell slightly in the quarter, to 4.7% of outstanding balances versus 4.8% in the prior quarter.