Most likely presidential action in response to this announcement would be the nomination for the next Supreme court justice.
Step-by-step explanation:
The Supreme court justice is the highest posted judge in the jury system of USA which is paramount for the third tenet of democracy to function well as the Post is the highest authority in terms of judicial decisions made.
So, as soon as the Supreme court justice resigns the government will start having to make a new Justice and the process of nominations and cross sectioning for the same as the system cannot remain without the chief justice.