I think the first task of a pope, as credited to Peter, is to strengthen all the faithful and pastors in the faith, or to confirm them in the true faith.
Regarding the current situation of the Church with the tremendous doctrinal confusion reigning in its life it is very evident. Therefore, this would be the most urgent act of the new pope.
He can do this through a magisterial act, in various forms such as an encyclical or apostolic constitution, and it should be done in a more solemn way to verify and rectify those issues in doctrine and morals which, especially in the last pontificate, were undermined and sometimes even denied.
So, I think this should be the most urgent act of the new pope.
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