Perhaps this is what photos are for: to remind us that we all appreciate beauty, that we all share a common desire for pleasure, for connection, for something that is greater than us.

也许这就是照片的作用：提醒我们都欣赏美丽的事物，提醒我们都想要得到快乐，想要与人联系，想变得更加优秀。

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This is the common desire of ASEAN countries and China.

这是东盟国家与中国的共同意愿。

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It is common desire of France and Britain to defeat the enemy.

战胜敌人是英国与法国的共同愿望。

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He spoke of America's desire for peace, and to seek the common good.

VOA: special.2009.01.24

Of course the most common use of the "I want to" pattern is when you express your desire for something.

当然，“I want to”句型最常见的用法是用来表达你对某事的愿望。

I want to 课堂 - SpeakingMax英语口语达人

Working Lives Kenya meets six people in very different social circumstances, but with a common desire to improve their lives.

BBC: Working Lives: Kenya

They have not, contrary to many pundits' claims, shared a common desire to have the state directing economic progress and private investment.

ECONOMIST: Asia and the abyss

So I think our meeting here today reflects the fact that we have a common desire for taking our responsibility in order to create a future with peace and prosperity.

WHITEHOUSE: President Obama Meets with Danish Prime Minister Rasmussen | The White House