吐故纳新 cast off the old and take in the new
Explanation
吐故纳新，原指人呼吸时，吐出浊气，吸进新鲜空气。现多指扬弃旧的、不好的，吸收新的、好的事物。比喻不断革新，吸收新的事物。
Originally, it referred to human breathing, exhaling stale air, and inhaling fresh air. Now it mostly refers to discarding the old and bad, absorbing the new and good things. It is a metaphor for continuous innovation and absorbing new things.
Origin Story
话说唐朝时期，有个书生名叫李白，他博览群书，尤其喜爱道家典籍。一日，他来到深山老林中，偶然发现一座道观。道观内，一位鹤发童颜的老道士正盘膝而坐，修炼吐纳之法。李白好奇上前请教，老道士笑着说："年轻人，你看这山间松柏常青，四季更替，皆因吐故纳新。人生亦如是，需不断学习新知，摒弃陈旧思想，方能进步。"李白听后深受启发，他明白，学习就像呼吸一样，要不断吐故纳新，才能保持生机活力，最终成就一番事业。后来，李白凭借其渊博的学识和对新知的渴求，成为了著名的诗仙。
It is said that during the Tang Dynasty, there was a scholar named Li Bai, who was well-read, especially fond of Taoist classics. One day, he came to a deep mountain and old forest, and accidentally found a Taoist temple. Inside the temple, an old Taoist with crane-hair and a childlike face was sitting cross-legged, practicing the method of breathing. Li Bai curiously went up to ask for advice, and the old Taoist smiled and said, "Young man, you see the pines and cypresses in the mountains are always green, the four seasons change, it is because of casting off the old and taking in the new. Life is also like this, it is necessary to constantly learn new knowledge and discard old ideas, in order to make progress." Li Bai was deeply inspired after listening, he understood that learning is like breathing, constantly casting off the old and taking in the new, in order to maintain vitality, and finally achieve a career. Later, Li Bai, with his profound knowledge and thirst for new knowledge, became the famous poet immortal.
Usage
吐故纳新常用来形容不断更新，吸收新的事物，多用于对人或事物发展变化的积极评价。
Tǔ gù nà xīn is often used to describe the continuous updating and absorption of new things, often used in positive evaluation of people or their development.
Examples
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他不断学习，吐故纳新，思想境界得到了很大的提高。
ta budúan xuéxí, tǔ gù nà xīn, sixiāng jìngjiè dédào le hěn dà de tígāo。
He continuously learns, casts off the old and takes in the new, his ideological realm has been greatly improved.
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这家公司积极引进先进技术，吐故纳新，保持了市场竞争力。
zhè jiā gōngsī jījí yǐnjìn xiānjìn jìshù, tǔ gù nà xīn, bǎochí le shìchǎng jìngzhēnglì。
The company actively introduces advanced technology, casting off the old and taking in the new, maintaining market competitiveness.