BEREA — On his first official day running the Cleveland Browns, Mike Holmgren presented coach Eric Mangini with some homework.

Mangini, known for popping quizzes on players, needs to study hard.

He has a huge test ahead.

Holmgren, looking unusually dapper in an expensive suit and tie, began his tenure as the Browns’ new president on Tuesday by granting Mangini at least one more day on the job. Holmgren did not have his much-anticipated sit down with Mangini, who ended an eventful first season in Cleveland with a four-game winning streak.

“I met with Eric briefly,” Holmgren said. “But not ’The Meeting.”’

That meeting will take place on Wednesday.

Holmgren, who stepped out of semiretirement for the challenge of rebuilding the Browns, said he didn’t want to rush Mangini into an important, career-defining meeting so soon after the completion of the season.

“I asked him to think about a few things this evening,” said Holmgren, who won a Super Bowl title with Green Bay and an NFC championship in Seattle during 17 seasons as a pro coach. “I did give him a list of things to think about for our meeting.”

Holmgren didn’t want his first day to be Mangini’s last.

Whether Mangini returns next season could hinge on whether he can work alongside Holmgren despite their differences in philosophy, personality, responsibility and vision. Holmgren knows the importance of a unified front and wants both men to lay everything on the table when they meet.

“I was a coach for a long time, it’s important he understands where I’m coming from and I understand where he’s coming from,” he said. “The only way you win in this league is when the coach and general manager are on the same wavelength. That’s the only chance.

“When egos get in the way, it destroys the team. My goal is to have everyone thinking in a like manner, going in the same direction. Let’s put the egos aside.”

Holmgren was asked if Mangini had a realistic chance of keeping his job.

“Absolutely,” he said. “Otherwise I wouldn’t have set the meeting up. I don’t dance too much. I appreciate people that shoot straight. We’re going to have a meeting and maybe a couple this week. But I hope to have that resolved by the end of the week.”

As for his own coaching future, Holmgren made it clear he has no intention putting the headset back on — for now.

“I’m not going to coach this team,” he said. “But in the offseason if someone wants to come in and talk football with me, I’d love that. I hope they do it. But I have a different gig now. I am not going to coach the football team. We’ll hire coaches to coach the football team.”

Holmgren is wasting no time getting back into the football trenches. He stepped down after last season to spend more time with his wife, Kathy, their four daughters and six grandchildren. But he’s back in the NFL and there’s plenty of work to be done.

In addition to his meeting with Mangini, Holmgren plans to interview Philadelphia general manager Tom Heckert for Cleveland’s GM opening. Heckert was granted permission to interview with the Browns last season, but the team instead hired George Kokinis, who was fired in November. Heckert’s father, Tom, was a scout for the Browns from 1982-86.

Holmgren said he has other GM candidates lined up for interviews but did not reveal any names.

Making his first public appearance since being hired by Browns owner Randy Lerner on Dec. 22, Holmgren was classic Holmgren: candid, composed and charming. He opened his remarks by joking that he hadn’t worn a tie to the previous “562 press conferences” and quickly acknowledged Browns Hall of Fame running back Jim Brown, who sat a few feet away clutching a cane.

While Holmgren’s appearance could spell doom for Mangini, Browns fans see his arrival as a fresh start. They’ve endured 11 seasons — only two with winning records — and have been waiting for someone like Holmgren to finally return their beloved team to prominence.

Holmgren did that in Green Bay, one of the few NFL cities that can match Cleveland’s football fervor. The job is daunting, but one Holmgren is embracing.

“I’m very, very excited to be here,” he said. “I’m excited about the possibilities of what we could do and understanding that any organization that has changed like this, can expect some change.”

Under Mangini, the Browns started 1-11 but won their final four games, a surge that at the very least bought him some time. Cleveland’s longest winning streak since 1994 under then-coach Bill Belichick may have shown Holmgren that Mangini has the Browns pointed in the right direction.

“The team finished strong,” Holmgren said. “But there’s a lot more to how this is going to play out than the last four games.”

And that could include off-the-field drama that served as a backdrop to Mangini’s 12 months in Cleveland. His institution of rules and discipline rubbed some players the wrong way, and he drew outside criticism when he fined one player $1,701 for not paying for a $3 bottle of water.

The league launched an investigation after rookie James Davis was injured during a post-practice “opportunity period” and veteran running back Jamal Davis blasted Mangini for working his players too hard. The Browns also had to fire Kokinis, Mangini’s hand-picked GM. Kokinis recently filed a $4 million arbitration case against the team, saying it didn’t allow him to fulfill duties outlined in his contract.

Most of that was washed over by the late surge, which included a win over Pittsburgh that snapped Cleveland’s 12-game losing streak to its rival.

Mangini was fired by the New York Jets after last season. If he’s dismissed again, he’ll be the first coach fired in consecutive full seasons by two different teams since Ray Rhodes, who was fired by Philadelphia in 1998 and Green Bay in 1999.