Kelly Wallace is CNN's digital correspondent and editor-at-large covering family, career and life. Read her other columns, and follow her reports at CNN Parents and on Twitter.

(CNN) When the Nice, France, attack was unfolding, I was on a train returning from a work assignment, trying to stay off my iPhone and BlackBerry so I could focus on writing a piece.

I arrived at Penn Station in New York City, looked at my devices and was stunned to see the alerts about yet another terrorist attack -- this time with a tractor-trailer used as a weapon of mass carnage.

Almost immediately, I felt anxious and couldn't wait to get far away from the station and back to my home. That feeling of "it could happen anywhere and anytime" took over. Think about what we've seen on the global stage over the past several months.

Orlando. Istanbul. San Bernardino, California. Brussels. Paris.

I thought back to a story I wrote after the San Bernardino attacks in which 14 people were killed. In that story, we explored how it's understandable that we adults feel anxious about the terror attacks and mass shootings and how those of us who are parents need to do whatever we can to not pass along our own anxiety about this scary and uncertain world to our children. But how do we do that?

I talked with some experts and believe their advice is as timely today as it was months ago.

"I think the problem is sometimes when adults feel very, very anxious, they tell themselves, 'Oh, as long as my kids are OK, I'm OK,' and so they then start to wonder, 'Are my kids OK?' " said Anderegg, a psychotherapist for children and adults in Lenox, Massachusetts.

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"You feel anxious so you check with your child, 'Do you feel anxious? Do you feel anxious?' Sooner or later, probably sooner, they will start to feel anxious."

Dr. Gail Saltz, associate professor of psychiatry at New York-Presbyterian Hospital, believes it's natural for parents to feel some anxiety, especially after a tragedy like a terror attack or a mass shooting, but what parents might not realize is how often children, beginning at the youngest ages, adopt coping mechanisms from watching us.

"They are used to you, and then in a time of crisis, they're looking to you for the cues, 'Are we safe?' and if you're running around going, 'Oh, I guess I don't feel comfortable going to work,' they're certainly going to feel that way as well," said Saltz, author of "Becoming Real: Defeating the Stories We Tell Ourselves That Hold Us Back." "You set the tone of what's safe and what's not."

What adults need to do when they feel anxious, such as after the last attack in Nice, in which 84 people were killed, including 10 children , is debrief in person -- not just on social media -- with other adults, said Anderegg, who is on the faculty in psychology at Bennington College.

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"If you feel anxious and you need to talk about your anxiety or the tragedy or your sadness or grief or the lack of meaning or whatever it is that you need to talk about, you need to talk to other adults before you talk to your children, because other adults are the proper place to process these kinds of adult feelings," he said. "So, my advice is don't use your child as your therapist."

Sure, it's OK to be honest with your kids and say you are feeling somewhat anxious, but sharing more information than they are equipped to process is only going to make them feel more on edge, he said.

"This does require some acting on our part and I think acting is fine," Anderegg said. "Because talking to 12-year-olds and saying, 'Oh my God, I'm really freaked out' ... is not appropriate, because kids can't do anything to keep themselves safe and all they can do is feel unsafe."

'Putting your own oxygen mask on first'

Taking care of our own anxiety that surfaces after a tragedy can be the best thing we can do to help our children feel safe, said Saltz.

"It's definitely a matter of putting your own oxygen mask on first, because you can best help your child if you've contained your own anxiety," she said. In addition to talking to other adults, anxious parents might embrace other anxiety-reducing activities such as aerobic exercise, deep breathing and hot baths. Turning off the nonstop news coverage also can help, she said.

"Not having it just so omnipresent, because you do increase the perception of frequency and then it gets harder to say, 'Hey, this is a rare event,' which it is," said Saltz.

Most anxieties are based on probability overestimation, said Anderegg. "You get on a plane and you think you are going to crash because you greatly overestimate the number of planes that actually crash," he said. Because the frequency of mass shootings in the United States has increased, some of us think they are more likely to happen, he added.

"But if we think about all the things that can harm people, a (mass shooting) is a very, very improbable event and seeing it on TV nonstop makes it feel more probable but doesn't make it actually more probable," he said.

Educating yourself about probability is one way to reduce your anxiety as a parent, said Anderegg, pointing to websites such as the Harvard Center for Risk Analysis, where you can look at how many people in the United States die every year in a mass shooting as compared to, for instance, traffic accidents.

"I'm phobic about planes but every time I get in one, I remind myself that it's really true you are much more likely to get killed in the car on the way to the airport than you are on a plane," he said.

Treating chronic parental anxiety

Parents with chronic anxiety are a different matter, Anderegg and Saltz agreed. These parents need to realize that without treatment, sooner or later, their anxiety will affect their children.

"Kids aren't stupid and they feel anxiety in a room," said Anderegg. He compared it to the different experiences of an infant, being held by someone who is anxious and who doesn't know what they are doing versus someone who is experienced and calm with babies.

"There's a huge difference ... babies can tell right away," he said. "Kids start from the earliest infancy being able to read the signals about whether or not the adults around them feel safe."

For their own health and the health of their children, parents with chronic anxiety disorders should get treatment, whether it's short- or long-term therapy or medication or both, said Anderegg.

There is a genetic predisposition to anxiety and it does run in families, said Saltz, so if parents are not aware of their own predispositions to it, they might not be able to pick up what's going on with their own child.

Some data also suggests that when both a parent and a child have an anxiety disorder and only the parent is treated, the child gets better, said Saltz, who co-presented a lecture on anxiety across all ages at New York-Presbyterian Hospital.

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"So, I'm not saying if a kid comes in with an anxiety disorder, they're going to say, 'Let's treat the parent,' but pretty much any clinician will say it would be much better for both the treatment now and prevention of future relapses if both got treatment, because if you remain having an anxiety disorder, it's going to be hard to help your child get better."

Being honest with your child about your chronic anxiety and showing them what steps you are taking to treat it, especially if anxiety runs in the family, can go a long way toward de-stigmatizing anxiety and treatment and equipping your child to deal with any anxiety they might encounter later on in life, said Saltz.

"Showing that it doesn't mean that you're weak or you're bad, it means this is an area of relative difficulty because you kind of want to prime a grownup who feels they can ask for help when they need it."