The parliamentary elections in Poland have just finished. The current ruling party Prawo i Sprawiedliwość has officially won the election, with 35.4% of the votes, but with only 194 seats they're well short of the 231 seat majority required to pass the vote of confidence (at least in the first attempt) and unlikely to build a ruling coalition. The "democratic opposition" (Koalicja Obywatelstwa, Trzecia Droga and Nowa Lewica) have 248 seats in total and have signalled that they would form a coalition but have no official agreement yet.
The president of Poland, Andrzej Duda, now has to designate the new Prime Minister and give them time to propose a new government. This can be any person (not even necessarily an MP) but it's typically a representative of the party that got a majority of votes. However, the president should consider their chances of building a successful government and passing the vote of confidence. There are following attempts possible if that vote fails but this question doesn't cover them.
This question is on who will be the first person designated by the President as the new Prime Minister. The choice is between:
Mateusz Morawiecki - the current Prime Minister from the ruling party PiS (and had been designated in the first attempt after the previous election in 2019)
Donald Tusk - the leader of the opposition party KO, which came second in the election with 30.7% of the votes
Someone else, including anyone from either parties (e.g. Jarosław Kaczyński)
@MrLuke255 I considered waiting until he's actually sworn in (initially I thought it'd happen just after the announcement but apparently it'll be on the 13th, when the new parliament assembles). But the linked president's address is fairly official and I think it satisfies the wording of the question ("ask" and "designate")