Every foreign tour by a head of state is a carefully sculpted and scripted affair. Every mark is measured in advance, every backdrop screened, every word weighed. Success is expected and the message carefully massaged so that there is rarely an alternative interpretation available.

Even by that admittedly low standard, U.S. President Barack Obama’s nine-day Asia tour in November should be regarded as a success. Mr. Obama’s tour served as a signal to the nations of the region — and the U.S. public — that their futures are deeply intertwined, that the United States will stay engaged, and that the belief that the U.S. is a declining power is wrong. It is a reassuring message for U.S. friends and partners.

In fact, Mr. Obama’s Asian sojourn began in Hawaii, when he hosted heads of state for the annual Asia Pacific Economic Cooperation (APEC) leaders meeting. While there are opinions that differ with the president over the value of the Trans-Pacific Partnership (TPP), Mr. Obama’s commitment to regional economic integration and the construction of mechanisms to build capacity and reinforce the rule of law in the Asia Pacific should be appreciated.

From Honolulu, Mr. Obama made his first visit to Australia as president (previous trips were canceled as a result of developments at home), where he and his host, Prime Minister Julia Gillard, reaffirmed their alliance and built upon it by announcing a stepped-up U.S. military presence in the north, consisting of marines and air and naval forces.

The move strengthens the U.S. capacity to stabilize and secure sea lanes in the Indian Ocean and the western Pacific. These waterways have always been important to Japan, but they are assuming a growing and more prominent role in the global economy.

From Australia, Mr. Obama returned to Indonesia, where he spent some of his formative years, and joined the annual meeting between the U.S. and the Association of Southeast Asian Nations and the sixth East Asian Summit (EAS), which was the first that the U.S. joined as a full participant. The president’s attendance at those two meetings was intended to signal the seriousness of the U.S. commitment to Southeast Asia and its institutions.

As Mr. Obama announced while attending the conferences, Secretary of State Hillary Clinton visited Myanmar last week, the first such visit by a ranking U.S. official. Myanmar has been a thorn in the side of successive U.S. administrations, but there have been signs of change in the reclusive country and Mr. Obama has decided that a gesture on his part is timely.

Recall that in his inaugural address, Mr. Obama called out to governments “on the wrong side of history,” saying that “we will extend a hand if you are willing to unclench your fist.”

While the indications of progress in Myanmar are still just hints of real reform, the dispatch of Mrs. Clinton is a signal as well to ASEAN that Washington is prepared to do more to be a better partner and work with its member governments to play a constructive role in the region.

Indeed, that is the real message of Mr. Obama’s trip: The U.S. is an integral part of the weave of nations in Asia and will continue to be deeply engaged. For many observers, this is a statement of the obvious. U.S. trade and investment in the region exceeds a trillion dollars annually, while hundreds of thousands of U.S. citizens reside in or visit the region on any given day. The U.S. has thick and thickening ties made manifest in the alliances, security partnerships and trade agreements that it has forged with regional governments.

Nevertheless, there is a belief that the U.S. is disengaging with Asia. The country’s economic woes in tandem with bitter partisan politics have reinforced the image of a nation distracted and diminished. As Washington struggles to put its house in order, there is a fear that it will disengage, pulling back military forces and focusing its efforts on getting its own house in order.

China’s rise is a poignant counterpoint to U.S. woes. Beijing is growing and confident, reaching out to regional governments to assure them — in good ways and bad — of its own enduring presence. Geography is sometimes destiny.

Chinese strategists are quick to label the U.S. a regional interloper whose thinking can change and has changed. Mr. Obama’s trip is intended to counter that message.

Not only is the U.S. committed to a regional presence — military, diplomatic and economic — but it is also engaging the region on Asian terms, investing in the diplomatic initiatives that regional governments have deemed important and valuable. The U.S. is listening.

While the U.S. has to attend to its own finances and settle its own affairs, it is a nation that has the capability to do both — restore its own health and stay intimately involved in the Asia-Pacific region.

A robust and engaged U.S. presence will not presage conflict with China. The U.S., like Japan, believes that the region is safer, more secure and has a brighter future working with Beijing rather than against it. Mr. Obama had a good trip. He — and his successor — are urged to return more often.

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