"This all moved a bit fast, so they both agreed to put it off," a source close to Pamela Anderson and Jon Peters tells PEOPLE

A source close to the former couple tells PEOPLE Anderson “just needed to take a step back” in deciding to split.

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“Although they have known each other for more than 30 years, they had never lived together,” says the source. “Living with someone, you truly get to know them. Pam’s a romantic, but she is also very independent.”

Adds the source, “This all moved a bit fast, so they both agreed to put it off.”

Image zoom Pamela Anderson and Jon Peters Pamela Anderson/Instagram

Anderson and Peters married on Jan. 20, with the Baywatch later announcing on Feb. 1 to The Hollywood Reporter that they had decided to split.

“I have been moved by the warm reception to Jon and my union,” the actress and activist, 52, said. “We would be very grateful for your support as we take some time apart to re-evaluate what we want from life and from one another. Life is a journey and love is a process. With that universal truth in mind, we have mutually decided to put off the formalization of our marriage certificate and put our faith in the process. Thank you for respecting our privacy.”

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A source told THR that the couple had not yet filed the legal paperwork for a marriage certificate after their wedding.

A rep for Anderson did not immediately respond to PEOPLE’s request for comment.

News of the split came just eight days after Anderson posted her first photo of she and Peters, 74, as a married couple to her Instagram Stories. In the photos, Anderson was beaming in the black and white shot, smiling next to Peters, who wore shades.

A day after their nuptials, Anderson’s publicist told PEOPLE, “They are very much in love and were married yesterday.”

Image zoom Jon Peters and Pamela Anderson in 1989 Ron Galella, Ltd./Ron Galella Collection via Getty

The two first met in the mid-’80s while at Hugh Hefner’s Playboy mansion and began dating after their encounter.

“Pamela has never seen her full potential as an artist. She has yet to shine in a real way. There is much more to her than meets the eye, or I wouldn’t love her so much,” Peters told THR after the nuptials. “”here are beautiful girls everywhere. I could have my pick, but — for 35 years — I’ve only wanted Pamela.”

“She makes me wild — in a good way. She inspires me. I protect her and treat her the way she deserves to be treated,” he continued.

Image zoom Pamela Anderson

Anderson was previously married to Tommy Lee, with whom she shares sons Brandon, 23, and Dylan, 22. The two were married from 1995 to 1998 and had a tumultuous marriage, in which Lee spent six months in the Los Angeles County Jail for spousal abuse.

The actress later married and divorced Kid Rock in 2006. Then she married and divorced producer Rick Solomon twice — in 2007 and 2013. Both marriages to Solomon dissolved in less than a year.

Peters, who produced both Barbra Streisand’s A Star Is Born in 1976 and the remake in 2018 with Bradley Cooper and Lady Gaga, was previously married to actress Lesley Ann Warren and producer Christine Forsyth-Peters.