Some states (including New York) have no Reconsideration phase. In these states, you must file a Request for Hearing before an Administrative Law Judge.)
If you are denied benefits at the initial level, you should appeal as soon as possible (within 60 days of the date on the denial notice). In most states, you do this by sending a letter to SSA telling them that you disagree with the decision or filling out a Request for Reconsideration (SSA-561)and mailing it to SSA.
The Reconsideration is a waste of time. In more than 90-percent of the cases SSA upholds the original decision. If you live in a state that requires the reconsideration phase, file the appeal and don’t submit any additional medical evidence. That will result in a quick denial which will allow you to request a hearing before an Administrative Law Judge.