In a PEOPLE exclusive interview, Zak, 37, details his new involvement with Inseparable, a mental health organization aiming to drive political change that ensures Americans everywhere are granted access to mental health care amid the coronavirus pandemic.
"Time flies," Zak says, reflecting they've celebrated six holidays without the Mrs. Doubtfire star. "I talked to my siblings to share stories and thoughts and photos that we like and appreciate."
He said that while the three of them are social distancing in their respective homes, "It will be nice to be able to speak with my brother and sister around remembering dad. It's certainly an opportunity to be introspective as we'll be together, apart."
"The key thing for us during this upcoming Father's Day is just to take some quiet time to reflect as a family around all the things that we're grateful for around him and who he was," Zak said.
Williams died at the age of 63 in August 2014 after suffering from Lewy Body Dementia, a type of brain disease that affected his thinking, memory and movement control. It’s the second-most common type of progressive dementia after Alzheimer’s disease.
In his own way, Zak has already found a way to reflect on his father's life and legacy by becoming an advocate for mental health after the star's death in August 2014.
Inseparable, for which Zak is on the Advisory Board, "is an organization supporting policy" for mental health programs, he says.
"The coronavirus pandemic has brought light to a parallel pandemic that's happening," says Zak. "We are experiencing from it as a direct result of the pandemic... a shared trauma that's becoming quite acute as a result of everything that people have been through both in terms of the devastating economic effects, the isolation and a lot of circumstances from communities."
RELATED VIDEO: Robin Williams' Youngest Son Gets Married on His Late Father's Birthday
He continues, "Instead of becoming more isolated, finding resentment, getting angry about it, we need to actually find solutions and opportunities to band together to find the resources and apply them to actual meaningful change on a system's level. That's what I think is so important at this time."
For his part, Zak's own method of finding peace and balance with his mental health has included "prioritizing self-care before I can show up for others," including his fiancée Olivia June and their 1-year-old son McLaurin Clement, whom they call Mickey.
"I stay away from drugs and alcohol, I commit to support groups," he says. "One thing I found very healing for me through my experience has been service and commitment to service work specifically around mental health and mental health support organizations. Eating well, committing to a healthy lifestyle. Things that I need in my weekly and daily regimen to better support my wellbeing."
His family is also a source of comfort; Zak says he's looking forward to spending time with Mickey on Father's Day.
"[Becoming a dad] completely changes [you], but [gives you] perspective on what it takes to actually show up for another person," he says. "To be a present and engaged parent requires focus and commitment to time and an effort that ... it's a lot. But the rewards are unlike anything I've experienced before."