New York Attorney General Andrew M. Cuomo announced the details of a new national database that would help determine how much insurance companies should reimburse patients who go out of network to see a doctor. Consumers would also be able to check a new Web site to see what an insurer was likely to pay before they went to an out-of-network doctor. The announcement is part of a settlement reached with more than a dozen insurance companies concerning the industry's controversial payment of out-of-network claims.