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For the first time since 2016, the Celtics’ season ended short of the conference finals. All the concerns ignited by the uneven regular season were crystallized when Boston was walloped by the Bucks in five games in the second round of the playoffs.

But there’s always next year, and for the Celtics’ front office, next year basically starts now, as it steps into one of the most important offseasons in franchise history.

The Celtics will try to convince two former All-Stars to stay, they will try to trade for a superstar, they will figure out what to do with up to four first-round draft picks, and they will try to assemble a roster that has better chemistry than the most recent one.

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Draft lottery Tuesday

The Celtics could have two lottery picks in next month’s draft, or they could have none. But their preference would be to have one.

Boston will receive the Kings’ pick as long as it does not land at No. 1 overall, in which case the 76ers will receive it and the Celtics will receive the 76ers’ pick. The Kings have the worst odds of any team in Tuesday’s lottery, with just a 1 percent chance of landing in the No. 1 spot and a 3.7 percent chance of falling in the 2-4 range, which would be Boston’s obvious preference.

The Celtics will receive the Grizzlies’ pick if it falls outside the top eight. Currently, Memphis sits in the No. 8 lottery position, but there is a 43.6 percent chance that it will be leapfrogged by a team behind it that gets some lottery luck. If that happens, the pick would roll over to next season, when it becomes top-six protected, before becoming unprotected in 2021. This is viewed as a weak draft, the Grizzlies are entering rebuild mode, the pick protections lighten moving forward, and the unknown of a future pick is always a more valuable trade asset, so the Celtics would rather not receive the pick this year.

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They also would not like to see Memphis vault to No. 1, where they could strengthen their team considerably by adding Duke’s Zion Williamson. And they do not want the Lakers or Knicks — two teams that could make a push for Anthony Davis — to vault to the top of the draft, where they would add a shiny asset to dangle.

NBA Combine Thursday-Friday

The NBA Combine, featuring many of the top draft prospects, will be held in Chicago Thursday and Friday. The Celtics would prefer to unload most of their picks in a Davis trade, but they must prepare as if they will end up having four first-round selections.

President of basketball operations Danny Ainge, who suffered a mild heart attack prior to Game 2 of the Bucks series, has been at the team’s training facility a few times recently, even sitting in on a couple of draft workouts. But it remains unclear if he will do any travel during the draft prep process, putting extra responsibility on the longtime core of assistant general manager Mike Zarren, director of player personnel Austin Ainge, and director of player evaluation Dave Lewin. The combine is filled with executives from each team, so it is also a place where trade discussions can begin to brew.

Opt-out dates

Kyrie Irving and Aron Baynes have until June 13 to opt into the final year of their respective contracts. Irving already has stated that he will opt out and forgo his $21.3 million salary, and there is no reason for him not to, because he will receive much more than that by signing a new max deal. It seems likely that Baynes will opt into the final year of his deal and claim the $5.4 million salary.

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Al Horford has until June 18 to opt into the final year of his deal, which would pay him $30.1 million next season. Horford’s situation is the most uncertain of the three. He turns 33 in a few weeks but remains probably one of the 30 best players in the NBA. He is unlikely to receive a deal that will pay more than $30 million next season, but he could prefer to opt out and sign a longer-term contract at a lower average salary for more long-term security.

He has hinted that his preference is to stay in Boston, but that might ultimately depend on what happens with Irving and the pursuit of Davis. Horford has never played in an NBA Finals, and if Boston switches back to its youth timeline, Horford could decide to go elsewhere.

Anthony Davis trade talks

Davis trade talks are where things become a bit tricky. A rule in the NBA’s collective bargaining agreement forbids teams from having two players on the roster who were acquired via trade after signing designated player extensions with their previous teams. Irving qualified when the Celtics traded for him two summers ago, so Boston must wait until he officially becomes a free agent on July 1 before trading for Davis.

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The issue for the Celtics is that any trade for Davis will likely include several picks in this year’s draft. So a handshake deal will have to be agreed upon prior to the June 20 draft so the Celtics know which players they will have to select for the Pelicans.

Boston’s hope, then, would be to have some clarity with Irving’s situation by then, as well as some sense from Davis’s camp about the possibility of him re-signing with the Celtics after he becomes a free agent next summer.

NBA Draft June 20

The Celtics are currently locked into the 20th, 22nd, and 51st overall picks in the draft. They will add at least one more first-round choice after the lottery, and perhaps two. These picks will be dangled in a potential Davis deal, but if one can’t be completed, things will get interesting.

The Celtics will not add five rookies to the roster next season. They could look to trade for a different veteran at a lesser cost, they could draft a player or two and stash them overseas, they could trade several picks in a package to move up in this draft, or they could trade picks in exchange for future picks.


Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him on Twitter @adamhimmelsbach.