We begin the brachah of Malchiyus with לך נקוה כן על. The first letters spell ן"עכ. Chazal tell us that Achan created this tefillah when he was taken to die. Chazal tell us the many sins that Achan committed. Why should we use the tefillah that he wrote? It is to teach us that even if we committed many aveiros, as many and as severe as Achan, we can do teshuvah and pronounce Hashem as King. Malchiyus begins with Achan's tefillah, so we will know that regardless of the past, with teshuvah, we become worthy of proclaiming Hashem is king, and Hashem will accept us.
Before tekiyas shofar, we recite Tehillim (47) קרח לבני למנצח, a psalm composed by Korach's children, who did teshuvah moments before they were swallowed into the earth. This, too, reminds us that regardless of our past, we can always do teshuvah. The children of Korach did teshuvah, and so can we.
