The Queen has highlighted the difficulty of remaining "calm and collected" in what is an "increasingly complex and demanding world".
Making her first major address since the UK voted for Brexit, she also stressed the need for political leaders to make "room for quiet thinking and contemplation" to deal with developments in a "fast-moving world".
The monarch spoke at the official opening of the fifth session of the Scottish Parliament, where First Minister Nicola Sturgeon stressed Scotland's determination to "play our part in a stronger Europe".
The ceremony was held just over a week after the UK voted to leave the European Union. But in Scotland the majority voted to remain, a result which prompted Ms Sturgeon to say a second independence referendum is now "highly likely".
While the Queen recognised the "fast moving" nature of events in her address, Ms Sturgeon chose to highlight Scotland's diversity as she recognised the role immigrants from across the world have played in both the past and present.
She spoke after the Queen, wearing a pale green and white outfit by Angela Kelly, told those at the ceremony: "Of course we all live and work in an increasingly complex and demanding world where events and developments can and do take place with remarkable speed, and retaining the ability to stay calm and collected can at times be hard.
"As this Parliament has successfully demonstrated over the years, one hallmark of leadership in such a fast-moving world is allowing sufficient room for quiet thinking and contemplation which can enable deeper consideration of how challenges and opportunities can be best addressed."
She also referred to new tax and welfare powers coming to Scotland in April 2017, telling MSPs: "I wish you every success as you prepare to take on these extra responsibilities and I remain confident you will use the powers at your disposal wisely and will continue to serve the interests of all the people of Scotland to the best of your ability."
Ms Sturgeon highlighted the need for Holyrood to be "bold and ambitious" and to "show courage and determination".
The First Minister added: "Our collective commitment to the people of Scotland today is that we will not shy away from any challenge we face, no matter how difficult or deep rooted."
She reflected on Scotland as a nation, saying: "We are more than five million men and women, adults, young people and children, each with our own life story and family history, and our own hopes and dreams.
"We are the grandchildren and the great grandchildren of the thousands who came from Ireland to work in our shipyards and in our factories
"We are the 80,000 Polish people, the 8,000 Lithuanians, the 7,000 each from France, Spain, Germany, Italy and Latvia. We are among the many from countries beyond our shores that we are so privileged to have living here amongst us.
"We are the more than half a million people born in England, Wales and Northern Ireland who have chosen to live here in Scotland. We are the thousands of European students studying at our universities and our colleges. We are the doctors and nurses from all across our continent and beyond who care for us daily in our National Health Service.
"Whether we have lived here for generations or are new Scots, from Europe, India, Pakistan, Africa and countries across the globe we are all of this and more. We are so much stronger for the diversity that shapes us.
"We are one Scotland and we are simply home to all of those who have chosen to live here, that is who and what we are."
Holyrood Presiding Officer Ken Macintosh said that despite "unprecedented political turbulence" brought by the referendum he had witnessed a "real willingness to work cooperatively and collaboratively" amongst politicians from different parties.
The vote for Brexit has had a "profound and dramatic impact on the political landscape" but Mr Macintosh said MSPs "stand at the brink of a new session with all the hope and promise that can bring".
The speeches were part of a day of celebration at Holyrood, with the ceremony also including music from the National Youth Choir of Scotland, the Royal Scottish National Orchestra Ensemble and Midge Ure. Scotland's national poet, the Makar Jackie Kay, read a specially-commissioned work.
Afterwards the leaders of Holyrood's five political parties headed outside to watch the ''Riding'' procession, a tradition that first took place in 1520 and continued until Parliament was abolished by the 1707 Act of Union.
Thousands of people lined Edinburgh's Royal Mile to see the 2,000 plus marchers, who included Shetland Vikings, members of the Polish and Punjabi communities, and a Chinese dragon, as well as traditional Highland dancers, pipe and brass bands.
The procession also included local heroes from communities across Scotland, each of whom had been nominated by one of the 129 MSPs.