How do Rob Pelinka and Kurt Rambis build a competitive Lakers team next season?

The Lakers were built on the hope this season that the Big Three of LeBron James, Anthony Davis and Russell Westbrook could deliver the franchise an NBA-best 18th championship.

The Lakers were also built on the hope that aging future Hall of Famers and role players had strong enough backs to be serious contenders for the crown.

It turned out to be false hope.

Now the question becomes how do Rob Pelinka, the Lakers’ vice president of basketball operations and general manager, and Kurt Rambis, the team’s senior basketball advisor, build a team for next season that will give their fans hope for better results following this disastrous season during which the Lakers were eliminated from NBA play-in tournament contention on Tuesday night in Phoenix.

James, Davis and Westbrook played just 21 games together this season because of multiple injuries to James and Davis. They went 11-10 in those games, hardly inspiring confidence that this was a championship-quality team.

Westbrook was asked late Tuesday night whether he‘d like to see what they can accomplish if healthy next season with that trio intact.

“Yeah. I mean, that’s the plan. But nothing is promised,” he said. “You kinda gotta take one day at a time each day. And like I’ve said all season long, you got to play the cards you’re dealt. Yes, we want to be able to see what that looks like, what that entails over the course of an 82-game season. But we’re not sure if that’s guaranteed neither. So, I just hope that we have a chance to be able to do something.”

Pelinka and Rambis will be challenged to put together a championship roster for next season that won’t be old and slow like this current underwhelming rendition.

The Lakers have just three players under contract for next season — James ($44.4 million), Davis ($37.9 million) and Talen Horton-Tucker ($10 million).

Two others have player options — Westbrook ($47.1 million) and Kendrick Nunn ($5.2 million).

Presumably, Westbrook will opt in, considering how much he’s due to earn, and so will Nunn, since he hasn’t played all season because of a bone bruise in his right knee.

The Lakers have a team option on Stanley Johnson ($2.3 million) and Austin Reaves ($1.5 million). They can give a qualifying offer to Mason Jones ($1.5 million), who is a restricted free agent after his two-way contract expires. They also have Wenyen Gabriel signed through next season on a two-way contract.

Role players Carmelo Anthony, Malik Monk, Trevor Ariza, Dwight Howard, Avery Bradley, Wayne Ellington and Kent Bazemore, who started the season with the Lakers and were expected to be contributors, will be unrestricted free agents, as will late-season acquisition D.J. Augustin.

Lakers guard Russell Westbrook brings the ball up during the first half against the Utah Jazz on March 31 in Salt Lake City.

(Rick Bowmer / Associated Press)

“A lot of our guys, besides maybe four or five, are on one-year deals, so that’s a personal choice for those guys,” Davis said about the group coming back en masse. “Like I said, when we put this team together, we had championship aspirations, and once again, injuries have gotten in the way of that.

“But I think you would love to see, I think the world would love to see, I think we would love to see what this team could be if we were healthy for the full 82. If that repeats next year, we have the same team, who knows? Like I said, we’ve got to recap this season — what worked, what didn’t work and go from there. But I truly think that we could have done something special if ‘Bron and myself, and mainly me, were healthy for the entire season.”

But they were not.

Davis missed almost six weeks because of a right mid-foot sprain before playing in the last three games.

James sat out for the fourth time in the last five games because of soreness in his left ankle.

How the Lakers improve the team will be interesting to see.

They don’t have a first-round draft pick until 2027. They are most likely looking at the taxpayer mid-level exception of about $6.4 million and veteran exceptions to sign players, much like last offseason.

They can look into trades, perhaps trying to move Westbrook this summer as the Lakers reportedly did before the trade deadline.

James can sign an extension with the Lakers on Aug. 4 worth up to about $97 million over two years.

And who will be the coach next season — Frank Vogel or someone else?

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Update: The Lakers listed James (left ankle), Davis (right mid-foot sprain) and Westbrook (right shoulder soreness) as questionable. The Lakers are trying to break a season-high seven-game losing streak. In the absence of the injured Stephen Curry (foot), Jordan Poole has been getting it done for the Warriors. Poole is averaging 18.4 points per game, shooting 36.8% from three-point range. Klay Thompson is averaging 19.3 points and Draymond Green is averaging 7.4 points, 7.4 rebounds and 7.0 assists per game.