But as yet, there is no clear sign if Labour will try to govern alone or enter some form of agreement with another party.
Carwyn Jones should be confirmed as first minister by the end of the week.
But who will serve in his government is a question yet to be answered.
Labour strategists are keeping all avenues open: These include serving as a minority government, forming a formal coalition or an informal arrangement with another party.
The party's election campaign manager, Pontypridd MP Owen Smith, said all options were available to them although he admitted a partnership with the Liberal Democrats might be "difficult".
Interim leader
"If they were to disavow Nick Clegg and renounce the right-wing policies that they are supporting in Westminster, we would be in a different situation," he told the BBC Politics Show.
He said Labour had worked well with Plaid Cymru during the previous coalition term but he said there were question marks over the party's direction.
The first task for assembly members will be to appoint a presiding officer.
Lord Dafydd Elis-Thomas is the front runner for another term for the position after Conservative David Melding ruled himself out.
After losing four seats, the weekend is likely to have given the Plaid leader Ieuan Wyn Jones some thinking time over his future.
The Conservatives in the assembly will start the process of appointing a permanent leadership successor to Nick Bourne, who lost his seat, on Wednesday.
The party has chosen Preseli Pembrokeshire AM Paul Davies as interim leader, but the permanent leader will not be confirmed until JUly.
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